Functional Analysis

Math 539 - Fall 2008 - #28025

1-2 PM, MWF, 307 Addams Hall

The aim of this course is to give an introduction to Functional Analysis, with a view towards applications in geometry, representation theory, C*-algebras and dynamical systems. In particular, we will cover aspects of the theory of Banach and Hilbert spaces, the Hahn-Banach theorem, the Open Mapping and Closed Graph Theorems, linear operators, compact operators and the spectral theorem for bounded operators on Hilbert space. As time permits, applications of these ideas to other fields will be discussed.

The following book will be the course text:

• "Functional Analysis; An Introduction" by Yuli Eidelman, Vitali Milman, Antonis Tsolomitis (Graduate Studies in Mathematics, Volume 66 - American Math Society) is a recent addition to the many classic texts on Functional Analysis. This book covers all the basic results with a minimum of prerequisites, and includes a huge number of exercises - with worked solutions!

• "Essential results of functional analysis" by Robert Zimmer (University of Chicago Press, 1990) is an excellent introduction to mordern topics in functional analysis related to applications in spectral geometry.