# Banach Lecture 20

This lecture (banach20) was given on 10/12/09.

### Excerpts

Let be an inf. dim’l Banach space, and let denote the ideal of compact operators. Then the Calkin Algebra is defined to be .

- is Fredholm iff its coset in the Calkin algebra is invertible.
- denotes the spectrum of the coset of in the Calkin algebra.

Prop II.3.2 if is Fredholm and is Fredholm and .

Rest of lecture has

- def of left and right Fredholm.
- Criterion for op. to be left or right Fredholm
- Def on an inner product
- Def of an inner product space
- Results on properties of inner product space
- Hilbert space: a complete inner product space.

Recall a topological space is separable if it contains a countable dense subset.

Advertisements

## About this entry

You’re currently reading “Banach Lecture 20,” an entry on Math Meandering

- Published:
- October 15, 2009 / 4:19 pm

- Category:
- Uncategorized

## No comments yet

Jump to comment form | comment rss [?] | trackback uri [?]