Category:Definitions/Star-Algebras

This category contains definitions related to Star-Algebras.
Related results can be found in Category:Star-Algebras.

Let $A = \struct {A_F, \oplus}$ be an unitary division algebra.

Let $A$ have a mapping $*: A_F \to A_F$ such that:

$\forall a \in A_F: \paren {a^*}^* = a$

$\forall a, b \in A_F: \paren {a \oplus b}^* = b^* \oplus a^*$

Then $A$ is a $*$-algebra (usually voiced star-algebra).