Category:Definitions/Nicely Normed Star-Algebras

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

Let $A = \struct {A_F, \oplus}$ be a star-algebra whose conjugation is denoted $*$.

Then $A$ is a nicely normed $*$-algebra if and only if:

$\forall a \in A: a + a^* \in \R$

$\forall a \in A, a \ne 0: 0 < a \oplus a^* = a^* \oplus a \in \R$