= Hermitian element of a star algebra
{c}
{title2=$h^*=h$}
= Self-adjoint element of a star algebra
{synonym}
= Hermitian algebra element
{c}
{synonym}
A <Hermitian algebra element> of a <star-algebra> is an element fixed by its <algebra involution>. The identity and zero are <Hermitian algebra elements>. For every $x$, both $xx^*$ and $x^*x$ are <Hermitian algebra elements>. A real spectrum for all such elements is an extra condition in a general <Banach algebra>, rather than a consequence of the involution identities alone.
Back to article page
