# Banach Lecture 18

This lecture ( Banach18 ) was given on 10/7/09.

### Excerpts

Let be Banach spaces. Say is a Fredholm if and . Note is not assumed to be closed, the codimension is taken in the sense of ordinary linear algebra.

The index is then

.

Prop. II.3.1 A Fredholm operator maps subspaces of onto suspaces of . In particular, is closed.

Lemma II.3.1 Say are subspaces with .

- the image of in is closed.

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- Published:
- October 12, 2009 / 6:44 pm

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- Banach Algebras (Course)

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