Normal element

In mathematics, an element of a *-algebra is called normal if it commutates with its adjoint.

{\displaystyle {\mathcal {A}}}

An element

is called normal if it commutes with

, i.e. it satisfies the equation

[1] The set of normal elements is denoted by

A special case of particular importance is the case where

is a complete normed *-algebra, that satisfies the C*-identity (

), which is called a C*-algebra.

be a normal element of a *-algebra

be a normal element of a C*-algebra