# Banach 24

This lecture (Banach24 ) was given on 10/21/09

### Excerpts

Definitions

- approximate eigenvalue
- Subspaces of a hilbert space that induce operators

Results

- Prop III.2.3, normal. Then (1) implies (2) All pts of are approximate eigenvalues, (3)
- Cor: self adjoint, then the in 1 is equal to and similarly for and .
- Prop. III.2.4 and a subspace with and is the orthogonal projection. Then (1) is T inv. iff , (2) is inv iff is inv. (3) induces iff .

There was a note about operator matrices.

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You’re currently reading “Banach 24,” an entry on Math Meandering

- Published:
- October 29, 2009 / 12:04 pm

- Category:
- Banach Algebras (Course)

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