Available Spring 2015
Math 6143, Functional Analysis, taught by Professor Alspach: Prerequisites: Real Analysis Math 5143-5153 or equivalent (abstract measure theory and integration, basic versions of the Hahn-Banach, Uniform Boundedness, and Open Mapping theorems, Hilbert spaces, representation of the duals of the L^p and C(K) spaces.)
Text: Peter Lax, Functional Analysis
The text covers or summarizes many topics in functional analysis. We will only cover a portion of the material. In the first part we will revisit some of the topics from functional analysis that are included in Math 5153 to get additional versions of the theorems, e.g., a geometrical separation version of Hahn-Banach, and a deeper understanding of convex sets, the relationships between standard spaces, and the use of duality. In the second part selected topics will be covered: operators on Hilbert spaces, particularly compact operators, an introduction to Banach algebras, and an introduction to distributions. Depending on the interests of the students in the class other topics or applications may be included as time allows.
Homework will be assigned and graded. This will be the principal method of assessment.