# Banach 29

This lecture (banach29 ;don’t mind the title) was given on 11/2/09

### Excerpts

functional calculus.

normal, for , is reducing subpsace of gen. by . Know is unit. equiv to , a Borel measure. For a bounded Borel measurable function can make sense of via

its well defined…

Review Rmk and

Lemma III.3.1 as above, then .

Lemma III.3.2 If and if is a Borel set then iff .

if implies .

Prop. III.3.3 s.t. for all

Such a measure is called a scalar spectral measure for .

and there’s another contstruction that I should understand better.

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## About this entry

You’re currently reading “Banach 29,” an entry on Math Meandering

- Published:
- November 3, 2009 / 11:08 am

- Category:
- Banach Algebras (Course)

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- red text

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