# Banach Lecture 16,17

These lectures ( Banach16&17) were given on 10/2/09, 10/5/09

### Excerpts

In these lecture the following result was proved.

Thm: Let is an infinite dimensional Banach space, is compact. If is nonempty then the set consists of eigenvalues of finite multiplicity (meaning is finite dimensional ) with no limit other than zero. This will follow from the following properties. With , , then

- is finite dimensional
- is closed and of finite codimension.
- such that ,
- and
- is invertible and is nilpotent or order

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- Published:
- October 5, 2009 / 5:50 pm

- Category:
- Banach Algebras (Course)

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