University of Leeds, School of Mathematics

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.

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