\begin{definition}[Definition:Nicely Normed Star-Algebra]
Let $A = \left({A_F, \oplus}\right)$ be a star-algebra whose conjugation is denoted $*$.
Then $A$ is a '''nicely normed $*$-algebra''' {{iff}}:
:$\forall a \in A: a + a^* \in \R$
:$\forall a \in A, a \ne 0: 0 < a \oplus a^* = a^* \oplus a \in \R$
\end{definition}