Messages from 1991
Date: Wed, 2 Jan 91 11:35 CST
From ALSPACH at NEMO.MATH.OKSTATE.EDU
Subject: Abstract of a paper by S. J. Montgomery-Smith
To: banach at NEMO.MATH.OKSTATE.EDU
X-VMS-To: IN%"banach at nemo.math.okstate.edu"
%This is the abstract of the paper "Comparison of Orlicz-Lorentz
%spaces" by S. J. Montgomery-Smith. It and the paper are in Plain TeX.
%The paper can be obtained by transmitting the message
% send [Banach]montsmithorlicz.tex
%to banach-files at nemo.math.okstate.edu
% Typeset this using plain-TeX
\centerline{\bf Comparison of Orlicz--Lorentz Spaces}
\medskip
\centerline{S.J.~Montgomery-Smith}
\bigskip
Orlicz--Lorentz spaces provide a common
generalization of Orlicz spaces and Lorentz spaces.
They have been studied by many authors, including
Masty\l o, Maligranda, and Kami\'nska. In this paper,
we consider the problem of comparing the
Orlicz--Lorentz norms, and establish necessary and
sufficient conditions for them to be equivalent. As a
corollary, we give necessary and sufficient
conditions for a Lorentz--Sharpley space to be
equivalent to an Orlicz space, extending results of
Lorentz and Raynaud. We also give an example of a
rearrangement invariant space that is not an
Orlicz--Lorentz space.
\bigskip
A.M.S.\ (1980) subject classification: 46E30.
\bye
Date: Tue, 5 Feb 1991 14:34:26 CST
From WBJ7835 at SUMMA.TAMU.EDU
Subject: A&MDeanSearch
To: ALSPACH at NEMO.MATH.OKSTATE.EDU
Message-Id: <910205143426.20c036bf at SUMMA.TAMU.EDU>
X-Vmsmail-To: SMTP%"ALSPACH at nemo.math.okstate.edu"
Dean, College of Science, Texas A&M University
The College of Science is comprised of the Departments of Biology,
Chemistry, Mathematics, Physics and Statistics, and the Cyclotron
Institute. The College has 270 faculty, 2,330 undergraduate majors, 778
graduate students, and a total research and teaching budget of
approximately $39,000,000. Ph.D. programs are offered in all
departments. Texas A&M University is a major teaching and research
institution and ranks in the top ten nationally in research funding, number
of national merit scholars, total student enrollment (41,000), and value of
its permanent endowment.
The successful applicant will have an outstanding record of achievement
in teaching and research and have demonstrable administrative skills.
Effective communication with multiple constituencies, a talent for
management of complex organizations, and a sense of visionary leadership
will be especially important.
Applications, consisting of a resume and the names of five persons from
whom we may request letters of reference, will be accepted until April
15, 1991, or until the position is filled. Women and minorities are
especially encouraged to apply.
Texas A&M University is an equal opportunity, affirmative action
employer.
Respond to: Dr. John A. Shadduck, Chair
Search Committee, Dean of Science
Texas A&M University
College Station TX 77843-4468
Phone: 409/845-3517
FAX: 409/845-6739
Mathematicians on Committee
J. Boone
S. Geller SCG6666 at tamvenus SCG6666 at venus.tamu.edu
W. B. Johnson wbj7835 at tamvenus wbj7835 at venus.tamu.edu
From NEMO::ALSPACH 27-FEB-1991 15:40:05.11
To: IN%"banach at nemo.math.okstate.edu"
CC: ALSPACH
Subject: Paper by N. Asmar and S. J. Montgomery-Smith
%This is the abstract of the paper "Almost everywhere convergence and
%distribution of Banach-valued Sidon series" by N. Asmar and
%S. J. Montgomery-Smith. The abstract and paper are in AMSTeX.
%The paper is available for downloading. Transmit the command
% send [banach]asmarmontsmith.atx
%to banach-files at nemo.math.okstate.edu.
% typeset using amstex
\def\beginsection#1\par{\vskip0pt plus.3\vsize\penalty-250
\vskip0pt plus-.3\vsize\bigskip\vskip\parskip
\centerline{{\bf #1}}\nobreak\smallskip\noindent}
\def\normo#1{\left\| #1 \right\|}
\def\widedot{\,\cdot\,}
\def\normdot{\normo{\widedot}}
\def\trinormo#1{\left|\left|\left| #1 \right|\right|\right|}
\def\trinormdot{\trinormo{\widedot}}
\def\snormo#1{\|#1\left.\kern-1.5pt\right\|}
\def\modo#1{\left| #1 \right|}
\def\smodo#1{|#1|}
%\def\Bbb#1{{\hbox{\bf #1}}}
\def\E{{\Bbb E}}
\def\N{{\Bbb N}}
\def\R{{\Bbb R}}
\def\C{{\Bbb C}}
\def\Z{{\Bbb Z}}
\def\P{\Cal P}
\centerline {Almost Everywhere Convergence and Distribution}
\centerline {of Banach-Valued Sidon Series}
\centerline {by}
\centerline {Nakhl\'e Asmar and Stephen Montgomery-Smith*}
\centerline{Department of Mathematics}
\centerline{University of Missouri}
\centerline{Columbia, Missouri 65211, U.S.A.}
\smallskip
\item{} A.M.S\ Classification (1980): 43A46, 43A15, 46E40.
\item{*}
Research supported by N.S.F.\ Grant D.M.S.\ 9001796.
\beginsection Summary
Let $B$\ be a Banach space, $G$\ a compact abelian group, $\Gamma$\ the dual
group of $G$, and $E$\ a Sidon subset of $\Gamma$. Denote by $\mu$\ the Haar
measure on $G$\ and by $\lambda$\ the normalized Lebesgue measure on $[0,1]$.
Using Pisier's recent characterizations of Sidon sets, we prove that there is a
constant $c>0$, that depends only on the Sidon constant of $E\cup(-E)$, such
that
$$
c^{-1} \lambda\left[\normo{\sum\limits^N_{n=1}a_nr_n}\geq c\alpha\right]
\leq \mu\left[\normo{\sum\limits^N_{n=1}a_n\gamma_n}\geq \alpha\right]
\leq c \lambda\left[\normo{\sum\limits^N_{n=1}a_nr_n}\geq c^{-1}
\alpha\right]
$$
for all $\alpha > 0$, where $a_1,\ldots,a_N$\ are arbitrary elements of $B$,
and $\gamma_1,\ldots,\gamma_N$\ are arbitrary elements of $E$.
In order to be able to make fruitful use of Pisier's results, we prove that the
Sidon constant of the ``$n$-fold join'' of $E$\ is uniformly bounded
independently of $n$.
We apply our results to derive new properties of Banach-valued Sidon series
that allow us to state necessary and sufficient conditions for the a.e.\
convergence of these series. Moreover, we obtain a principle of contraction of
Banach-valued Sidon series, and lower bound estimates on the distribution
functions of the scalar-valued version of these series.
\bye
Date: Mon, 25 Mar 91 14:52:08 +1000
From iand at hydra.maths.unsw.oz.AU
To: banach-list at NEMO.MATH.OKSTATE.EDU
Message-Id: <9103250452.AA01979 at hydra.maths.unsw.OZ.AU>
Subject: Conference on PROBABILITY AND ANALYSIS
Announcing a mini-conference
PROBABILITY AND ANALYSIS
at
The University of New South Wales
Sydney, Australia
24 - 26 July, 1991
The main topics of this conference will be the use of probability in
analysis, and geometric and operator theoretic aspects of Banach space
theory. This may include topics such as the use of martingale
techniques in the study of singular integrals, the behaviour of
partial differential operators on $L^p$ spaces, or the study of
contractive projections on Banach spaces.
Participants will include
A. Pelczynski (Polish Academy of Science),
D.L. Burkholder (Illinois-Urbana), E. Albrecht (Saarbrucken),
A. McIntosh (Macquarie/C.M.A.), G. Gaudry (Flinders), G. Brown,
M. Cowling, I. Doust, B. Jefferies, W. Ricker (U.N.S.W.)
and B. Sims (Newcastle).
The conference proceedings will be published as a volume of the
Proceedings of the Centre for Mathematics and its Applications (A.N.U.).
Anyone interested in attending should contact the organisers as soon
as possible, in order that suitable accommodation near the University
might be arranged. As a guide, college accommodation is likely to
cost about AU$50 per night (bed and breakfast); motels rooms near the
University are AU$65 per night (room only) and upwards. There will be
a small registration fee.
Please send requests for further information to
Ian Doust
School of Mathematics
University of New South Wales
Kensington, N.S.W., 2033,
Australia.
Phone: 61-(0)2-692 2970.
Fax: 61-(0)2-662 6445.
E-mail: iand at hydra.maths.unsw.oz.au.
This meeting is supported by
The Centre for Mathematics and its Applications, A.N.U.,
(formerly the Centre for Mathematical Analysis)
and
The University of New South Wales
From NEMO::ALSPACH 25-MAR-1991 16:14:34.70
To: IN%"banach at nemo.math.okstate.edu"
CC: ALSPACH
Subject: Paper by E. Odell
%This is the abstract of the paper "On Schreier unconditional
%sequences" by E. Odell. The paper and abstract are in plain TeX. The
%paper may be downloaded by transmitting the command
% send [banach]odellschreier.tex
%to banach-files at nemo.math.okstate.edu.
% 3/22/91: Paper by E. Odell in plain.tex (UT-Austin)
% UT Math Imagen printer parameters
%\voffset=1truein \hoffset=1truein
%%%%%%%%%%% My defs %%%%%%%%%%%%%%%%%
\font\caps=cmcsc10
\def\blackbox{\hbox{\vrule width6pt height7pt depth1pt}}
\def\qed{~\hfill~\blackbox\medskip}
\def\IR{\mathop{{\rm I}\kern-.2em{\rm R}}\nolimits}
\def\nat{\mathop{{\rm I}\kern-.2em{\rm N}}\nolimits}
\def\A{{\cal A}} \def\F{{\cal F}}
\def\varep{\varepsilon}
\def\ov{\overline}
\def\myskip{\noalign{\vskip6pt}}
\def\hangbox to #1 #2{\vskip1pt\hangindent #1\noindent \hbox to #1
{#2}$\!\!$}
\def\myitem#1{\hangbox to 30pt {#1\hfill}}
%%%%%%%%%%% Preliminary info begins here %%%%%%%%%
\centerline{\bf On Schreier Unconditional Sequences}
\bigskip
\centerline{{\caps E. Odell}\footnote*
{Research partially supported by the National Science Foundation
Grant DMS-8903197.}}
\medskip
\centerline{Department of Mathematics}
\centerline{The University of Texas at Austin}
\centerline{Austin, Texas 78712}
\vskip.3in
{\narrower\smallskip\noindent
{\bf Abstract.} Let $(x_n)$ be a normalized weakly null sequence in a Banach
space and let $\varep>0$. We show that there exists a subsequence
$(y_n)$ with the following property:
$$\hbox{ if }\ (a_i)\subseteq \IR\ \hbox{ and }\ F\subseteq \nat$$
satisfies $\min F\le |F|$ then
$$\big\|\sum_{i\in F} a_i y_i\big\| \le (2+\varep) \big\| \sum a_iy_i\big\|\ .
$$
Date: Mon, 8 Apr 91 09:30 CST
From ALSPACH at NEMO.MATH.OKSTATE.EDU
To: banach at NEMO.MATH.OKSTATE.EDU
X-VMS-To: IN%"banach at nemo.math.okstate.edu"
Subject: Paper by T. Schlumprecht
%This is the abstract of the paper "An arbitrarily distortable Banach
%space" by T. Schlumprecht. The paper and abstract are in plain TeX.
% The paper may be downloaded by transmitting the command
% send [banach]schlumprecht.tex
% to banach-files at nemo.math.okstate.edu.
% 4/3/91: Author: Thomas Schlumprecht
% Title: An Arbitrarily Distortable Banach Space
% File prepared using plain.tex at UT-Austin, Math Dept
% Contact M. Combs (combs at math.utexas.edu) for TeX questions on file.
%%%%%%% UT-Math printer parameters %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\magnification=\magstep1
\voffset=1truein \hoffset=1truein
%%%%%%% My defs -- Change with Care %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\font\caps=cmcsc10
\font\titlefont=cmbx10 scaled \magstep2
\def\title#1{\centerline{\titlefont#1}\bigskip}
\def\author#1{\centerline{\caps #1}\smallskip}
\def\Math{\centerline{Department of Mathematics}}
\def\UT{\centerline{The University of Texas at Austin}}
\def\Austin{\centerline{Austin, Texas 78712}}
%%%%%%% TOP MATTER STARTS HERE %%%%%%%%%%%%%%%%%%%%%%%%%%%%
\topinsert\vskip.5in\endinsert
\title{An Arbitrarily Distortable Banach Space}
\author{Thomas Schlumprecht}
\Math
\UT
\Austin
\vskip.3in
{\narrower\smallskip\noindent
{\bf Abstract}.
In this work we construct a ``Tsirelson like Banach space''
which is arbitrarily distortable.\smallskip}
From NEMO::ALSPACH 12-APR-1991 08:07:35.51
To: IN%"banach at nemo.math.okstate.edu"
CC: ALSPACH
Subject: Abstracts of two papers
%This is the abstract of the paper "Non dentable sets in Banach spaces
%with separable dual" by S. Argyros and I. Deliyanni. The abstract and paper
%are typed in AMSTeX. The paper may be downloaded by transmitting the command
% send [banach]argyrosdeliyanni.atx
%to banach-files at nemo.math.okstate.edu.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentstyle{amsppt}
\magnification =1200
\topmatter
\title Non Dentable Sets in Banach Spaces With Separable Dual
\endtitle
\author Spiros A. Argyros and Irene Deliyanni\\
(Herakleion Crete)\endauthor
\abstract{A non RNP Banach space E is constructed such that $E^{*}$
is separable and RNP is equivalent to PCP on the subsets of E.}
\endtopmatter
%This is the abstract of the paper "Level sets and the uniqueness of
%measures" by D. Alspach. The paper and abstract are in AMSTeX. The
%paper may be downloaded by transmitting the command
% send [banach]alspachmeasures.atx
%to banach-files at nemo.math.okstate.edu.
%%%%%%%%%%%%%
\documentstyle{amsppt}
\magnification =1200
\title Level Sets and the Uniqueness of Measures
\endtitle
\author Dale E. Alspach\thanks{Research supported in part
by NSF grant DMS-8902327.}\endauthor
\address{
Department of Mathematics
Oklahoma State University
Stillwater, OK 74078-0613}
\abstract{A result of Nymann is extended to
show that a positive $\sigma$-finite measure with
range an interval is determined by its level sets.
An example is given of two finite positive
measures with range the same finite union of intervals but
with the property that one is
determined by its level sets and the other is not.}
\endtopmatter
Date: Fri, 19 Apr 91 13:01 CST
From ALSPACH at NEMO.MATH.OKSTATE.EDU
Subject: UTAMIRFAS
To: banach at NEMO.MATH.OKSTATE.EDU
X-VMS-To: IN%"banach at nemo.math.okstate.edu"
FIRST ANNOUNCEMENT OF SPRING UTAMIRFAS
The U.T.-A&M Informal Regional Functional Analysis Seminar
will meet Saturday, May 4 and Sunday, May 5 at Texas
A&M in College Station. Talks will be in Milner Hall 101.
Tentative Schedule
Saturday, May 4
9:30 Coffee & Donuts, Milner 317
10:00 T. Figiel, Texas A&M University, Best constants in Rosenthal's
inequality: the case p > 4
11:15 A. Arias, Weizmann Institute, Primarity of $c_1$ and
applications to nest algebras
12:15 Break for lunch
2:00 S. Agyros, Oklahoma State University, Representations
of convex, nondentable sets
3:30 D. E. Alspach, Oklahoma State University, Level sets and the
uniqueness of measures
5:30 Swimming party & dinner at Jan & Bill Johnson's
Sunday, May 5
9:00 Coffee & Donuts, Milner 317
9:30 T. Schlumprecht, University of Texas, A complementably-
minimal Banach space not containing $l_p$ or $c_o$
10:45 V. Paulsen, University of Houston, Representations of function
algebras and Banach space geometry
We expect to be able to cover housing for a small number of
participants. Preference will be given to participants who do
not have other sources of support, such as sponsored research
grants.
Here are some local motels. I'll be happy to make reservations.
If you make reservations yourself, ask for A&M and government
rates.
In Southwood Valley, where most local participants live:
Quality Inn, 2514 Texas Av S, (409) 696-6988,
Manor House Inn, 2504 Texas Av S, (409) 764-9540,
Ponderosa Motor Inn, 3702 Texas Av S, (409) 693-6810.
On campus:
Memorial Student Center Guest Rooms, (409) 845-8909.
Near campus, but not fun to walk:
Hampton Inn, 320 Texas Av S, (409) 846-0184,
La Quinta Inn, 607 Texas Av S, (409) 696-5900,
Holiday Inn, 1503 Texas Av S, (409) 693-1736,
Comfort Inn, 104 Texas Av S, (409) 846-733,
Western Motel, 204 Texas Av S, (409) 846-5757.
Generally considered the top place in town:
Hilton, 801 University Dr E, (409) 693-7500.
Next door to Hilton:
Inn at Chimney Hill, 901 University Dr E (409) 260-9150.
Some motels include some kind of breakfast and/or cocktails
(e.g., Comfort Inn; Hampton Inn; Inn at Chimney Hill; Manor
House) with the room.
Bill Johnson
wbj7835 at tamvenus (preferred)
(409) 845-2722 office
(409) 696-2812 home
From NEMO::ALSPACH 29-APR-1991 17:01:13.43
To: IN%"banach at nemo.math.okstate.edu"
CC: ALSPACH
Subject: paper by Jesus Bastero and Francisco J. Ruiz
%This is the abstract of the paper "Interpolation of operators when the
%extreme spaces are $L^\infty$" by Jesus Bastero and Francisco J. Ruiz.
%The paper is available for downloading. Transmit the command
% send [banach]basteroruiz.tex
%to banach-files at nemo.math.okstate.edu.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% PLAINTEX, textures 1.01
\magnification=1200
\def\R{\hbox{$I\kern-3.5pt R$}}
\def\N{\hbox{$I\kern-3.5pt N$}}
\def\V{\Vert}
\font\fp=cmr8
\def\P{{\noindent \it Proof.- }}
\def\fin{ Q.E.D. \medskip}
\def\sign{\rm sign}
\def\var{\overline\va}
\hsize=15true cm
\hoffset=0.5true cm
\vsize=23true cm
\def\va{\varphi}
\centerline{\bf INTERPOLATION OF OPERATORS WHEN THE EXTREME}
\centerline {\bf SPACES ARE $L^\infty$}
\bigskip
\centerline {by}
\bigskip
\centerline{ Jes\'us Bastero\footnote
*{\fp Research partially supported by DGICYT PS87-0059} and Francisco J.
Ruiz\footnote {**}{\fp Research partially supported by DGICYT
PB89-0181-C02-02} }
\bigskip
\midinsert
\narrower\narrower
\noindent ABSTRACT. {\sl In this paper, equivalence between interpolation
properties of linear operators and monotonicity conditions are studied, for a
pair $(X_0,X_1)$ of rearrangement invariant quasi Banach spaces, when the
extreme spaces of the interpolation are $L^\infty$ and a pair $(A_0,A_1)$
under
some assumptions. Weak and restricted weak intermediate spaces fall in our
context. Applications to classical Lorentz and Lorentz-Orlicz spaces are
given.}
\endinsert
\bigskip
\bye
From NEMO::ALSPACH 24-MAY-1991 01:45:41.98
To: IN%"banach at nemo.math.okstate.edu"
CC: ALSPACH
Subject: International Research Workshop On Banach Space Theory
Preliminary Announcement
International Research Workshop On Banach Space Theory
Merida, Venezuela, January 6-17, 1992
The Workshop is sponsored by International Mathematical Union and
support from NSF is pending.
For information, contact
Bor-Luh Lin
University of Iowa
Iowa City,IA,52242
e-mail:bllin at math.uiowa.edu
phone# 319-335-0784;fax# 319-335-0627.
Bor-Luh Lin
From NEMO::ALSPACH 31-MAY-1991 15:02:35.47
To: IN%"banach at nemo.math.okstate.edu"
CC: ALSPACH
Subject: Paper by G. Pisier
%This is the abstract of the paper "Remarks on complemented subspaces
%of von-Neumann algebras" by G. Pisier. The abstract and paper are in
%plain TeX. The paper may be downloaded by sending the message
% send [banach]pisiervonneumann.tex
%to banach-files at nemo.math.okstate.edu.
\magnification\magstep1
\baselineskip=18pt
\centerline{{\bf Remarks on complemented subspaces of von-Neumann
algebras}\footnote*{Supported in part by N.S.F. grant
DMS 9003550}} \vskip12pt \centerline {by Gilles Pisier}
\vskip12pt \centerline {Texas A. and M. University and
Universit\'e Paris 6} \vskip12pt
{\bf Abstract}
In this note we include two remarks about
bounded ($\underline{not}$ necessarily contractive) linear projections on
a von Neumann-algebra. We show that if $M$ is a
von Neumann-subalgebra of $B(H)$ which is complemented in
B(H) and isomorphic to $M \otimes M$ then $M$ is injective
(or equivalently $M$ is contractively complemented). We do
not know how to get rid of the second assumption on $M$.
In the second part,we show that any complemented
reflexive subspace of a $C^*$- algebra is necessarily
linearly isomorphic to a Hilbert space.
\vfill\eject
From NEMO::ALSPACH 4-JUN-1991 10:27:17.77
To: IN%"banach at nemo.math.okstate.edu"
CC: ALSPACH
Subject: Paper by G. Pisier
%This is the abstract of the paper "Interpolation between H^p spaces
%and non-commutative generalizations I" by G. Pisier.
%The abstract and paper are in plain TeX. The paper may be downloaded
%by sending the command
% send [banach]pisierinterpol.tex
%to banach-files at nemo.math.okstate.edu.
\magnification\magstep1
\baselineskip=18pt
\def\w{\widetilde}
\def\i{\infty}
\def\v{\vert}
\def\V{\Vert}
\centerline{{\bf Interpolation Between
$H^p$ Spaces and Non-Commutative
Generalizations I}\footnote*{Supported in part by N.S.F.
grant DMS 9003550}} \vskip12pt \centerline {by Gilles
Pisier} \vskip12pt
{\bf Abstract}
We give an elementary proof that the $H^p$ spaces over
the unit disc (or the upper half plane) are the
interpolation spaces for the real method of interpolation
between $H^1$ and $H^{\infty}$. This was originally
proved by Peter Jones. The proof uses only the boundedness
of the Hilbert transform and the classical factorisation
of a function in $H^p$ as a product of two functions in
$H^q$ and $H^r$ with ${1/q}+{1/r}=1/p$. This proof
extends without any real extra difficulty to the
non-commutative setting and to several Banach space
valued extensions of $H^p$ spaces. In particular, this
proof easily extends to the
couple $H^{p_{0}}(\ell_{q_0}),H^{p_{1}}(\ell_{q_1}) $,
with $1\leq p_{0}, p_{1}, q_{0}, q_{1} \leq \infty$. In
that situation, we prove that
the real
interpolation spaces and the K-functional are induced ( up
to equivalence of norms ) by the same objects for the
couple $L_{p_0}(\ell_{q_0}),L_{p_1}(\ell_{q_1}) $. In an
other direction, let us denote by $C_p$ the space of all
compact operators $x$ on
Hilbert space such that $tr(|x|^p) <\infty$. Let $T_p$
be the subspace of all upper triangular matrices
relative to the canonical basis.
If
$p=\infty$, $C_p$ is just the space of all compact
operators. Our proof allows us to show for instance that
the space $H^p(C_p)$ (resp. $T_p$) is the interpolation
space of parameter $(1/p,p)$ between $H^1(C_1)$
(resp. $T_1$) and $H^\infty(C_\infty)$ (resp. $T_\i$). We
also prove a similar result for the complex
interpolation method. Moreover, extending a recent
result of Kaftal-Larson and Weiss, we prove that the
distance to the subspace of upper triangular matrices in
$C_1$ and $C_\infty$ can be essentially realized
simultaneously by the same element.
From NEMO::ALSPACH 3-JUN-1991 11:51:48.92
To: IN%"banach at nemo.math.okstate.edu"
CC: ALSPACH
Subject: Paper by G. Pisier
%This is the abstract of the paper "A simple proof of a theorem of Jean
%Bourgain" by G. Pisier. The abstract and paper are in plain TeX. The
%paper may be downloaded by sending the command
% send [banach]pisierdisc.tex
%to banach-files at nemo.math.okstate.edu
\magnification\magstep1
\baselineskip=18pt
\let\a=\i
\centerline{{\bf A simple proof of a
theorem of Jean Bourgain}\footnote*{Supported in part by
N.S.F. grant DMS 9003550}} \vskip12pt \centerline {by G.
Pisier} \vskip12pt
{\bf Abstract.}
We give a simple proof of Bourgain's disc algebra version
of Grothendieck's theorem, i.e. that every operator on the
disc algebra with values in $L_1$
or $L_2$ is 2-absolutely summing and hence extends to an
operator defined on the whole of $C$. This implies
Bourgain's result that $L_1/H^1$ is of cotype 2. We
also prove more generally that $L_r/H^r$ is of cotype
2 for $0<r< 1$.
\vfill\eject
Date: Mon, 10 Jun 91 08:46 CST
From ALSPACH at NEMO.MATH.OKSTATE.EDU
Subject: Position at Missouri
To: banach at NEMO.MATH.OKSTATE.EDU
X-VMS-To: IN%"banach at nemo.math.okstate.edu"
Date: Fri, 07 Jun 91 18:06:24 CDT
From: MATHUMC%umcvmb.missouri.edu at relay.cs.NET
To: banach-list%nemo.math.okstate.edu at relay.cs.NET
Dear Colleague(s):
If you know someone who will be intersted in the following job
please let me know. This is a teaching/service job.
Thanks,
Elias Saab
POSITION AVAILABLE
Applications are invited for the following position starting
August 1, 1991. Instructor of Mathematics, Masters degree
with demonstrated potential for excellence in undergraduate
instruction is essential. Experience with computers, PCs,
MACINTOSHES and IBM mainframes, is required. The duties of
the position include: Coordinating Math 10 (College
Algebra), teaching two three hour courses in each of the
fall and winter semesters, assisting the Director of
Undergraduate Studies. This is a nine month renewable
appointment that requires availability Monday through
Friday. A complete application consists of a letter of
application, vita, and at least three letters of
recommendation. All materials should be sent to
Elias Saab, Chair, Department of Mathematics, University
of Missouri, Columbia, MO 65211.
E-mail mathumc at umcvmb.missouri.edu
University of Missouri is an Equal Opportunity Employer.
Date: Tue, 9 Jul 91 11:56 CST
From ALSPACH at NEMO.MATH.OKSTATE.EDU
Subject: A new Ghoussoub
To: banach at NEMO.MATH.OKSTATE.EDU
X-VMS-To: IN%"banach at nemo.math.okstate.edu"
Date: Fri, 5 Jul 1991 13:10:49 CDT
From: WBJ7835 at sigma.tamu.EDU
Subject: baby
To: banach-list at NEMO.MATH.OKSTATE.EDU
Message-Id: <910705131049.2140bd35 at SIGMA.TAMU.EDU>
X-Vmsmail-To: SMTP%"banach-list at nemo.math.okstate.edu"
Louise and Nassif Ghoussoub (userghou at ubcmtsg.bitnet; 4472 Crown St.,
Vancouver, B.C., Canada; (604) 224-6918) are pleased to
announce the birth of their daughter Mireille Fleury Ghoussoub on
July 4, 1991 at 7:50 p.m. Mother and seven pound baby are doing fine;
proud father is reportedly in happy-shock.
Date: Tue, 9 Jul 91 13:09 CST
From ALSPACH at NEMO.MATH.OKSTATE.EDU
Subject: Message from Globevnik about Yugoslavia
To: banach at NEMO.MATH.OKSTATE.EDU
X-VMS-To: IN%"banach at nemo.math.okstate.edu"
From: IN%"aron%mcs.kent.edu at relay.cs.NET" 5-JUL-1991 14:39:36.17
To: alspach%nemo.math.okstate.edu at relay.cs.NET
CC:
Subj:
>From josip.globevnik at uni-lj.ac.mail.yu Tue Jul 2 12:33:20 1991
Received: from ixgate.gmd.de by encore.mcs.kent.edu (5.64+/10.12.90)
id AA12225; Tue, 2 Jul 91 12:33:07 -0400
Received: by ixgate.gmd.de id AA12236; Tue, 2 Jul 91 18:33:40 +0200
Date: 2 Jul 91 13:30 +0200
From: Josip Globevnik <josip.globevnik at uni-lj.ac.mail.yu>
To: aron at mcs.kent.edu
Message-Id: <425:josip.globevnik at uni-lj.ac.mail.yu>
Subject: Attack
Status: RO
Dear Richard,
please forward this message to all people who know me or my work.
Best regards
Josip
==================
Date: 2 Jul 91 13:24 +0200
From: fnimfm05 at uni-lj.ac.mail.yu
To: josip.globevnik at uni-lj.ac.mail.yu
Message-ID: <421:josip.globevnik at uni-lj.ac.mail.yu>
Subject:
From: VEGA::GLOBEVNIKR 2-JUL-1991 13:22:24.28
To: UEK::FNIMFM05
CC:
Subj:
From: VEGA::GLOBEVNIKR 2-JUL-1991 13:25
To: GLOBEVNIKR
Subj:
I apologize as at this time my message has not much to do with
mathematics, except perhaps in the sense that the question of survival
of Slovenes is also connected with survival of Slovene mathematics.
As you know, Yugoslav federal army began a brutal attack on Slovenia
which includes bombings. The attack was encouraged by the official
opinions of US and EEC that the integrity of Yugoslavia has the top
priority in their approaches to solving the crisis in Yugoslavia.
It suited very well the communist regimes in Serbia and Montenegro
which see the rest of Yugoslavia as greater Serbia which should become
a communist country and which have very strong influence on the
Yugoslav army. The fight between the federal army and the Slovene
army is thus the fight between the remaining communist forces and
the newly established democracy in Slovenia. It is of utmost
importance for the crisis in Yugoslavia that the official opinions
about integrity of Yugoslavia are finally changed to recognizing that
the tensions in Yugoslavia are much too great to keep Yugoslavia in
one piece, except perhaps by a brutal force which the west has
always condemned and which neglects human rights
and the right to selfdetermination of every nation and free choice
about with whom and how it wands to establish relations.
The west should get strongly involved in a controlled dissintegration
of Yugoslavia. The first step towards this would be the official re-
cognition of the independent and sovereign state of Slovenia. The
public opinion has been changing in this direction but the official
opinions seem to follow these changes too slowly.
Since the official opinion of the west is one of the principal
reasons for the encouragement to use the brutal force in Slovenia
I would be most grateful if you could use all your available communi-
cation channels to convey this message to your government, your
media or any relevant institution. I would be most grateful also if
you can support Slovenia by adding your personal support to this
message.
I would also appreciate if you forward this message to any
colleague of yours who knows me or who is familiar with my work in
mathematics as my mailing list here is very short. With my best regards
With my best regards
Josip Globevnik
email josip.globevnik at uni-lj.ac.mail.yu
PS For the case that you are more interested I am providing some details.
As you may have heard, the Republic of Slovenia had a plebiscite
last December on which more than 90% of the people voted that they
wanted that Slovenia becomes an independent and sovereign state.
Since that time the Slovene parlament (a multiparty parlament that
was elected on free elections in spring a year ago) had been preparing
the legislature on the basis of which Slovenia would become an inde-
pendent and sovereign state by June 26, half a year from plebiscite.
The slovene government and the slovene presidency have been proposing
negotiations about this to other republics and to the federal autori-
ties several times since last December but there was almost no response
to these proposals.
Slovenes, a small nation of two million people have never had any
conflict with any other nation. We are hard working (I am a tipical
example of a Slovene), peaceful people who would only want to live
in their own state as this would guarantee that we ourselves would
make decisions in the foreign policy and have control at the outflow
of our own money. We have not had border problems with Croatia, the
only Yugoslav republic that has border with Slovenia. Our mentality
is similar to the mentality of people in the nearby Austria. We are
culturally part of western culture. We now have a western type parla-
mentary system and would like to become a part of integrated Europe.
Slovenia became an independent and sovereign state on June 25.
On June 27, early in the morning, the federal army's tanks were
rolling in different directions out of army posts in Slovenia,
mainly towards Ljubljana airport and towards the border crossings
on boredrs with Austria and Italy to cut off Slovenia from their
western and northern neighbours. It was clear that the Yugoslav
army decided to attack brutally in Slovenia. The Slovene army,
armed with antitank and antihelicopter missiles began to fight fiercely
as it is defending our home. The Yugoslav army in Slovenia collapsed
and their units have been blocked since by the Slovene army. Alrea-
dy during the second day of fight the Yugoslav army bombed the town
of Dravograd, near austrian border. The agreement between Yugoslav
prime minister Markovic and Slovene prime minister Peterle was reached
yesterday night that army was to move back into its barracks under
the supervision of a special technical committee that was yet to be
formed. However, the Yugoslav army started moving before such committee
was ever formed and this provoked new clashes with Slovene army. New
bombings took place this morning. (Slovenes have no airplanes to fight
against such bombings). Now the Yugoslav army reserve has been called
in Serbia consisting entirely of Serbs are approaching Slovenia.
From Alspach Dale <alspach>
To: banach
Subject: Abstract of a paper by B. Khaoulani and Note about
AMSTeX
Message-Id: <91Jul23.194723cdt.8 at hardy.math.okstate.edu>
Date: Tue, 23 Jul 1991 19:47:07 -0500
% This is the abstract of the paper
%"A Gordon-Chevet type Inequality
% by
%B. Khaoulani
%It and the paper are typed in AMSTeX. The paper may be
downloaded
%from the bulletin board by transmitting the command
% send khaoulani.atx
%to: banach-files at hardy.math.okstate.edu.
\documentstyle{amsppt}
\topmatter
\title
A Gordon-Chevet type inequality
\endtitle
\author
B. Khaoulani \footnote{Universit\'e Paris VII, URA 1321,
1990-91.}
\endauthor
\abstract{ We prove a new inequality for Gaussian processes, this
inequality implies the Gordon-Chevet inequality. Some remarks on
Gaussian
proofs of Dvoretzky's theorem are given.}
\endtopmatter
\document
\bye
%%%%%IMPORTANT NOTE ABOUT
COMPATIBILITY%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%This paper is not compatible with AMSTeX 2.0 but is compatible
with earlier
%versions. Because the new AMSTeX is not compatible with earlier
versions
%papers in AMSTeX should state at the beginning which version is
to be used.
%Papers typed for one version will only be mildly incompatible
with other %versions if \define is
%used sparingly and specific font files are not used. The AMS has
changed
%font files several times and compatibility has been maintained
only at
%the top level, e.g., \bf always gives boldface but the actual
font
% file and point size is determined by the structure and
implementation of
%the version of TeX and AMSTeX.
From Alspach Dale <alspach>
To: banach
Subject: Email address for G. Godefroy
Message-Id: <91Jul24.092451cdt.8 at hardy.math.okstate.edu>
Date: Wed, 24 Jul 1991 09:24:48 -0500
Date: Tue, 23 Jul 1991 22:11:17 -0500
From: elias at esaab.cs.missouri.edu (Elias Saab)
Message-Id:
<9107240311.AA02150 at esaab.cs.missouri.edu.cs.missouri.edu>
To: banach-files at hardy.math.okstate.edu
Cc: alspach at hilbert.math.okstate.edu
Distribute
Dear Colleague:
This is to tell you that Gilles Godefroy left Missouri now and
his new
E-mail address is:
gig at ccr.jussieu.fr
Thanks,
Elias Saab
From alspach Fri Sep 13 15:39:33 1991
To: banach
Subject: Abstract of a paper by D. Leung and Note
This is the abstract of the paper "Banach spaces with Property (w)"
by Denny Leung.
The paper is typed in LATeX. The paper may be downloaded
from the bulletin board by ftp or transmitting the command
send leungpropw.ltx
to: banach-files at hardy.math.okstate.edu.
A Banach space E is said to have Property (w) if every (bounded
linear) operator from E into E' is weakly compact. We give some
interesting examples of James type Banach spaces with Property (w). We
also consider the passing of Property (w) from E to C(K,E).
------------------------------------------------------------
Note: I will be away from Sept. 14 until Sept. 23 -Dale Alspach
From alspach Mon Sep 23 09:20:19 1991
To: banach
Subject: Research group on Quantitative Estimates for Polynomials
\magnification 1200
\nopagenumbers
\vskip1cm
Bernard Beauzamy \hfill Per Enflo, Paul Wang
Institut de Calcul Math\'ematique \hfill Kent State University
Paris, France. \hfill Kent, Ohio
\vskip1cm
\centerline{wish to develop their research group on}
\vskip1cm
\centerline{\bf Quantitative estimates for polynomials in one or several variables}
\vskip1cm
and they encourage applications for Ph.D. studies (Th\`ese) in this direction.
\vskip0.5cm
The topic has direct applications to Analysis (Fourier Analysis, Harmonic
Analysis), to Number Theory, and Computer Science (Symbolic Computation,
Massively Parallel Programming). It is supported by the
{\it National Science Foundation} (U.S.A.), the {\it C.N.R.S.} (France),
the Ministry of Defense (France), and {\it DIGITAL Eq. Corp.}.
\vskip1cm
The applicants should be citizens either of the U.S. or of one of the
countries of the European Community. They will have to work either in
Paris or in Kent, and may have to travel between both places.
\vskip1cm
Please write to :
\vskip.5cm
Prof. Bernard Beauzamy, Institut de Calcul Math\'ematique,
Universit\'e de Paris 7, 2 Place Jussieu, 75251 Paris CEDEX 05, France,
\vskip0.5cm
or to
\vskip.5cm
Prof. Per Enflo, Prof. Paul Wang, Department of Mathematical Sciences,
Kent State University, Kent, Ohio 44242, U.S.A.
\end
From alspach Mon Sep 23 09:31:40 1991
To: banach
Subject: Email address for B. Maurey and others
----- Begin Included Message -----
Date: Sat, 21 Sep 1991 05:46:18 -0500
From: MAUREY%FRMAP711.BITNET at CUNYVM.CUNY.EDU
To: alspach at hilbert.math.okstate.edu
Message-Id: <91Sep21.035408cdt.5 at hardy.math.okstate.edu>
Status: R
The machine supporting FRMAP711 will disappear on Sept. 24th;
addresses for Pajor, Khaoulani, Beauzamy, Maurey will be changing.
Bernard.
----- End Included Message -----
I will send out new addresses as soon as learn of them. -Dale
From alspach Tue Sep 10 08:44:33 1991
To: banach
Subject: Conference in Venezuela
Status: R
The workshop on Banach space theory in Merida, Venezuela, Jan 6-17
has received funding from NSF, CONICIT and IMU. If you are interested
in attending this workshop, contact Bor-Luh (Peter) Lin,
bllin at math.uiowa.edu, for more information.
From alspach Thu Sep 5 13:15:23 1991
To: banach
Subject: abstract of a paper by G.Pisier . (with abstract !)
This is the abstract of the paper "The K_t-functional for
the
interpolation couple L_1(A_0),L_infinity(A_1)" by Gilles Pisier
The paper is typed in TeX. The paper may be downloaded from
the bulletin board by ftp or by transmitting the command
send pisierktinterpol.tex
to: banach-files at hardy.math.okstate.edu.
Let (A_0,A_1) be a compatible couple of Banach spaces in the
interpolation
theory sense. We give a formula for the K_t-functional of the
interpolation
couples (l_1(A_0),c_0(A_1)) or (l_1(A_0),l_infinity(A_1)) and
(L_1(A_0),L_infinity(A_1)).
From Alspach Dale <alspach>
To: banach
Subject: Summary of Gowers-Maurey results
Message-Id: <91Sep26.132550cdt.5 at hardy.math.okstate.edu>
Date: Thu, 26 Sep 1991 13:25:41 -0500
Dear subscribers,
I asked Tim Gowers and Bernard Maurey to make up a
sort of abstract of their results for distribution on the
bulletin
board since the interest in them is so great. Here is a note from
Bernard Maurey that I received today.
Dale Alspach
----- Begin Included Message -----
From: MAUREY%FRCIRP81.BITNET at CUNYVM.CUNY.EDU
Subject: UBSP
To: alspach at hilbert.math.okstate.edu, MAUREY at frcirp81.bitnet
Status: R
Tim Gowers and the author of these lines independently solved
the
Unconditional Basic Sequence Problem in the negative;
(Tim's solution was the first to appear); we produced
almost identical examples of an infinite dimensional
Banach space $X$ that does not contain any infinite
unconditional
basic sequence; we decided to publish jointly the final version
of this example and to work together to find more properties of
this
space.
It was observed by Bill Johnson that our space $X$ is
Hereditarily
Indecomposable, which means that no closed subspace of $X$ is the
topological sum of two infinite dimensional closed subspaces.
This property obviously implies that $X$ does not contain any
infinite unconditional basic sequence.
The space $X$ is reflexive, has a monotone basis,
and it is possible to show that the
dual $X^*$ is also H.I. We proved that complex H.I. spaces have
few operators: every operator on a complex H.I. space can be
written
as $T= \lambda Id + S$, where $S$ is strictly singular; the
spectrum
of $T$ is finite or consists of a converging sequence of
eigenvalues
with finite multiplicity (together with the limit). It follows
that a complex H.I. space is not isomorphic to any proper
subspace, in particular not isomorphic to its hyperplanes.
Since we may build our space on the complex field, this provides
a second (negative) solution to the hyperplane problem, that was
first solved by Tim Gowers.
B. Maurey.
From Alspach Dale <alspach>
To: banach
Subject: Gowers preliminary version of the solution of the UBSP
Message-Id: <91Oct7.115040cdt.45464 at hardy.math.okstate.edu>
Date: Mon, 7 Oct 1991 11:50:37 -0500
Dear Subscribers,
Tim Gowers has made available his version of the solution to
the unconditional basic sequence problem. The file is in Plain TeX but
uses mssymb.tex. If you have upgraded to AMSTeX 2.0 and changed the fonts,
you may not be able to use mssymb. To overcome this input amssymb.def and
amssym.tex as indicated in the file.
To obtain the file use ftp or transmit the command
send gowersubsp.tex
to banach-files at hardy.math.okstate.edu
Dale Alspach
From Alspach Dale <alspach>
To: banach
Subject: gowersubsp.tex
Message-Id: <91Oct10.120836cdt.46210 at hardy.math.okstate.edu>
Date: Thu, 10 Oct 1991 12:08:32 -0500
Dear Subscribers,
We believe we have found the problem with gowersubsp.tex. The software
has trouble with files of over 50K length. We are looking for a better
way to handle these files but as a temporary solution all files of
length over 50K will be split. For TeX files I will add
\input lines to the first part of the file which use the banach-files names
for the remaining parts. For example gowersubsp.tex has been split into
gowersubsp1.tex and gowersubsp2.tex. The last line of gowersubsp1.tex is
\input gowersubsp2.tex. If you change the names or concatenate the files you
will need to fix this. Also you will need to request the pieces in two
email messages, else the software will try to assemble the pieces into
a single file, find that it is too long, and send only the first.
In summary to get Tim Gowers TeX file send two email messages to
banach-files at hardy.math.okstate.edu
First message
send gowersubsp1.tex
Second message
send gowersubsp2.tex
Alert me to any further problems. I will also be splitting the older files
of length greater than 50K.
Dale Alspach
From Alspach Dale <alspach>
To: banach
Subject: Abstract of a paper by Cole, Gamelin and Johnson
Message-Id: <91Oct11.094903cdt.46539 at hardy.math.okstate.edu>
Date: Fri, 11 Oct 1991 09:49:01 -0500
This is the abstract of the paper " Analytic Disks in Fibers over the Unit Ball of a Banach Space" by B.J. Cole, T.W. Gamelin, and W.B. Johnson. The paper is typed in AMSTeX. The paper may be downloaded
from the bulletin board by ftp or transmitting the commands in separate messages
send colegamjohn1.atx
and
send colegamjohn2.atx
to: banach-files at hardy.math.okstate.edu.
We study biorthogonal sequences with special properties, such as
weak or weak-star convergence to 0, and obtain an extension of the
Josefson-Nissenzweig theorem. This result is applied to embed analytic
disks in the fiber over 0 of the spectrum of H^infinity (B), the algebra of
bounded analytic functions on the unit ball B of an arbitrary infinite
dimensional Banach space. Various other embedding theorems are
obtained. For instance, if the Banach space is superreflexive, then
the unit ball of a Hilbert space of uncountable dimension can be
embedded analytically in the fiber over 0 via an embedding which is
uniformly bicontinuous with respect to the Gleason metric.
From Alspach Dale <alspach>
To: banach
Subject: Position at Missouri
Message-Id: <91Oct30.093912cst.45785 at hardy.math.okstate.edu>
Date: Wed, 30 Oct 1991 09:39:00 -0600
Date: Tue, 29 Oct 1991 12:28:52 -0600
From: "Elias Saab" <MATHUMC%UMCVMB.BITNET at uga.cc.uga.edu>
To: Alspach_Dale <alspach at hilbert.math.okstate.edu>
Subject: Advertising for a position.
Message-Id: <91Oct29.123344cst.46049 at hardy.math.okstate.edu>
Please let me know if somebody is interested in the job described
below. One of the areas in our department is
Harmonic Analysis and this is one of the areas we
will try to hire in.
Thank you.
Elias Saab
UNIVERSITY OF MISSOURI
DEPARTMENT OF MATHEMATICS
COLUMBIA, MO 65211
E-mail MATHUMC at UMCVMB.MISSOURI.EDU
Applications are invited for one tenure-track position at the
rank of assistant professor beginning in August of 1992. The
position requires a PH.D., quality teaching, and a commitment
to a distinguished research career. Selections for the position
will be based primarily on demonstrated research achievement in an
area complementary to areas of ongoing departmental research.
Send a curriculum vitae along with a letter of application
(include E-mail address), and arrange for three letters of
recommendation to be sent to: Professor E. Saab, Chair, at the
address above. The application deadline is December 31, 1991,
or until the position is filled thereafter. Applications received
after February 1, 1992, cannot be guaranteed consideration.
Women and minorities are encouraged to apply. AA/EEO.
From banach-owner Wed Oct 30 16:52:11 1991
Received: by hardy.math.okstate.edu id <45794>; Wed, 30 Oct 1991 16:37:06 -0600
From Alspach Dale <alspach>
To: banach
Subject: Position at Bowling Green State U
Message-Id: <91Oct30.163706cst.45794 at hardy.math.okstate.edu>
Date: Wed, 30 Oct 1991 16:36:53 -0600
Date: Wed, 30 Oct 1991 16:28:33 -0600
From: neal carothers <carother at andy.bgsu.edu>
Message-Id: <9110302228.AA06979 at andy.bgsu.edu>
To: alspach at hardy.math.okstate.edu
Subject: Position at BGSU
Assistant Professor, Tenure-Track
Bowling Green State University
Department of Mathematics and Statistics
Bowling Green, OH 43402-0221
Prof. A.W.M. Glass, Chair
The Department seeks qualified applicants for an anticipated
tenure-track position in FUNCTIONAL ANALYSIS, APPLIED ANALYSIS,
or COMPUTATIONAL MATHEMATICS. We have a growing PhD program
and seek to strengthen these areas. The position carries a
two-course teaching load (6 to 8 semester hours) and requires
a PhD in Mathematics. In addition, the selected candidate
will be expected to pursue research, work with doctoral students
and eventually direct dissertations. Preference will be given
to candidates with a strong research record, and whose research
is compatible with our current faculty. Salary competitive.
Please provide vita, publication list, official transcript, and
arrange to have three letters of recommendation sent by
February 1, 1992 to Prof. Glass (at the above address).
By way of a brief description of BGSU, we really DO have a growing
PhD program -- 13 PhD's awarded over the last three years, 8 more
expected in the next two years. We are a short one-hour drive
from Ann Arbor, two-and-a-half hours from Ohio State, and three hours
from Kent. Our library is quite good and the University has been
reasonably generous about providing personal computers (and access
to mainframes). Active research interests include Banach Space
Theory, Operator Theory, Function Theory, Optimization, and
Scientific Computation (FEM, etc). For more information, please
don't hesitate to write, call, or e-mail either:
Neal Carothers OR Steve Seubert
carother at andy.bgsu.edu sseuber at andy.bgsu.edu
(419) 372-8317 (419) 372-2179
From alspach Tue Dec 10 13:15:54 1991
To: banach
Subject: abstract of a paper by N. Asmar and S. Montgomery-Smith
This is the abstract of the paper "On the distribution of Sidon series"
by N. Asmar and S. Montgomery-Smith. The paper is typed in LaTeX.
The paper may be downloaded from the bulletin board by ftp or
transmitting the command
send asmarmontsmith.ltx
to: banach-files at hardy.math.okstate.edu.
This is a revision of asmarmontsmith.atx .
%LaTex document
\documentstyle[12pt]{article}
\def\Bbb#1{{\hbox{\bf #1}}}\def\N{\Bbb N}\def\R{\Bbb R}\def\C{\Bbb C}
\def\Z{\Bbb Z}\def\Con{${\cal C}$}\def\M{${\cal M}$}\def\T{\Bbb T}
\begin{document}
\title{On the Distribution of Sidon Series}
\author{Nakhl\'e H.\ Asmar and Stephen Montgomery-Smith
\\ University of Missouri--Columbia \\ Columbia, MO 65211 \\ U.\ S.\ A.
\date{}}
\maketitle
\begin{abstract}
Let $B$ denote an arbitrary Banach space, $G$\ a compact abelian group
with Haar measure $\mu$\ and
dual group $\Gamma$. Let $E$ be a Sidon subset of $\Gamma$ with Sidon
constant $S(E)$. Let
$r_n$ denote the $n$-th Rademacher function on $[0 , 1]$.
We show that there is a constant $c$, depending only on $S(E)$, such
that, for all $\alpha > 0$:
\begin{eqnarray*}
c^{-1}P\left[\left\| \sum_{n=1}^Na_nr_n\right\| \geq
c\alpha \right] & \leq &
\mu\left[ \left\|
\sum_{n=1}^Na_n\gamma_n\right\|\geq \alpha \right]
\\
& & \leq \
c\,P\left[\left\| \sum_{n=1}^Na_nr_n\right\| \geq c^{-1}\alpha
\right]
\end{eqnarray*}
where $a_1$, $\ldots$ , $a_N$ are arbitrary elements of $B$,
and $\gamma_1$ ,
$\ldots$ , $\gamma_N$ are arbitrary elements of $E$. We prove a similar
result for Sidon subsets of dual objects of compact groups,
and apply our results to
obtain new lower bounds for the distribution functions of scalar-valued
Sidon series.
This paper is a rewrite of a paper previously submitted to the noticeboard.
\end{abstract}
\end{document}
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