# Banach Lecture 12

This lecture (banach12) was given on 9/23/09

### Excerpts

is unital -algebra, is normal element. closed subalgebra gen. by polynomial in ; its commutative.

where (think about this, it makes sense). This map is injective, surjective, algebra isomorphism, and preserves involution.

Extremely disconnected: closure of every open set is open.

Prop I.9.5 is a unital Banach algebra, is closed untial sub alg. . Then either or is the union of bnd complementary components of .

Prop I.9.6 is a unital alg. , untial alg, . Then .

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- Published:
- September 24, 2009 / 7:51 pm

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- Banach Algebras (Course)

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