# Banach Lecture 11

The lecture: banach11

### Excerpts

Unless otherwise specified, is a unital -alg.

Prop. I.9.1 If is a normal element (commutes with adjoint) in a alg. then .

Prop I.9.2 If is self adjoint, then .

Prop I.9.3 If is commutative then .

Thm I.9.1 If is commuative, then . The Gelfond transform is an isometry and it intertwines the involution with complex conjugation.

Cor. is nonunital, commutative then is loc. compact and .

Prop. I.9.4 Let be commutative and assume polynomial in are dense in . The gives homemorphism and .

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You’re currently reading “Banach Lecture 11,” an entry on Math Meandering

- Published:
- September 21, 2009 / 7:55 pm

- Category:
- Banach Algebras (Course)

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