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.

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