# Banach 26

This lecture (Banach26) was given on 10/26/09

### Excerpts

Results

finished proof of 1

1. Thm III.3.1 Every cyclic normal op. unit. equiv. to Canonical Multiplication Operator (CMO).
2. Thm III.3.2 (spec. thm. for normal op.) Version 1: Every normal op. $T$ on $H$ is unit. equiv to a direct sum of CMO’s.

Some examples were given, specifically about the shift operator on $l^2(\mathbb{Z})$.  The spetrum of the shift operator is $\mathbb{T}$, the unit circle.