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University of Leeds, School of Mathematics

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Graduate course in Analysis

**Time:** Tuesdays 12-1 and 2-3,
from September 30th to December 9th 2003

**Place:** Room G, School of Mathematics, University of Leeds

**Lecturer:**
Prof. J.R. Partington

The course will fall into two fairly independent halves. I aim to
cover the following topics in as much detail as time permits:

**1. Banach space theory **

*Bases in Banach spaces. Convexity and smoothness properties.
Weak topologies and reflexivity. *

**2. Operator theory**

*Isometries, Wold decomposition, universal models.
Normal operators and spectral theory.
Functional calculus. The invariant subspace problem.
*

Prerequisites: some familiarity with Hilbert spaces,
elementary operator theory, and the standard examples of Banach spaces.

Last updated
September 5th 2003