Fall 2006:  202, Functional Analysis

Course: MAT-202-1, CRN 43695
Instructor: Roman Vershynin
    e-mail: vershynin at math dot ucdavis dot edu
    Office hours: M 1-2, W 2-3 in 2218 MSB
Meeting times: MWF 11:00 - 11:50.
Location: BAINER 1128

Yuli Eidelman, Vitali Milman, Antonis Tsolomitis, Functional analysis. An introduction. Graduate Studies in Mathematics, 66. American Mathematical Society, Providence, RI, 2004. xvi+323 pp. ISBN 0-8218-3646-3

Monographs for further reading and references:

Course description:

  1. Fundamental theorems of functional analysis. Open mapping theorem. Closed graph theorem. Projections in Banach spaces. Banach-Steinhaus theorem. Applications to constructing counterexamples in Fourier analysis. Hahn-Banach theorem. Separation of convex sets. Alaoglu theorem. Eberlein-Smulian theorem. Extremal points and Krein-Milman theorem. [Chapter 9]
  2. Compact operators (Review Section 4.3). Adjoint operators; Shauder's duality theorem (Section 4.4). Spectrum of linear operators on Banach spaces. Fredholm theory of compact operators [Chapter 5]
  3. Functions of operators. Spectral theory of self-adjoint bounded operators on Hilbert space. [Chapter7]

Prerequisites: MAT 201 A,B

Problem Set 1 (50%),
Problem Set 2 (50%)
Homework from the textbook: