# nLab commutative C-star-algebra

Contents

### Context

#### Algebra

higher algebra

universal algebra

# Contents

## Idea

A commutative $C^\ast$-algebra is a C-star algebra whose underlying associative algebra is a commutative algebra.

## Properties

### Relation to topological spaces

Commutative $C^\ast$-algebras are those identified by Gelfand duality with algebras of continuous functions on compact Hausdorff topological spaces.

### Relation to KK-theory

###### Example

Every commutative C-algebra is a nuclear C*-algebra.

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Last revised on July 23, 2018 at 06:28:44. See the history of this page for a list of all contributions to it.