# nLab normal operator

### Context

#### Algebra

higher algebra

universal algebra

# Contents

## Definition

An element $a \in A$ in a C-star algebra is called normal of its commutes with its star-adjoint:

$a a^* = a^* a \,.$

## Properties

The spectral theorem asserts, roughly, that (bounded) normal operators can be diagonalized

Created on March 16, 2011 15:02:02 by Urs Schreiber (46.144.132.190)