MATH 7132: Functional Analysis
Spring 1997. University of Colorado Denver

PREREQUISITE:
MATH 6131: Introduction to Real Analysis, or with instructor's approval

HOURS: TR 6:55-8:10 pm, Bravo 656

INSTRUCTOR:
Prof. Andrew Knyazev
Office: CU (Dravo) 644. Phone: 556-8102.
Office hours: Wed 3pm - 6pm (or by appointment)
WWW: http://math.ucdenver.edu/~aknyazev

TEXTBOOK:
E. Kreyszig, Intoductory Functional Analysis with applications. John Wiley & Sons, 1989.

SUBJECT:
Linear metric and normed spaces, duality, spaces of functions, linear operators, compact operators, elements of spectral theory.

CONTENTS:
The class will follow the outline below, touching on each major topic in a depth that will be determined by the pace of the class.

• Ch 1. Metric Spaces
• Ch 2. Normed Spaces. Banach Spaces
• Ch 3. Inner Product Spaces. Hilbert Spaces
• Ch 4. Fundamental Theorems for Normed and Banach Spaces
• Ch 5. Further Applications: Banach Fixed Point Theorem
• Ch 7. Spectral Theory of Linear Operators in Normed Spaces
• Ch 8. Compact Linear Operators on Normed Spaces and Their Spectrum

MIDTERM TEST - FINAL TEST