Definition 6.4.1.label Let $A$ be an involutive Banach algebra. An element $x\in A$ is said to be self-adjoint or hermitian if $x=x^{*}$; normal if $x^{*}x=xx^{*}$; unitary if $x^{*}x=xx^{*}=1$ when $A$ is unital; a projection if $x^{2}=x$ and $x^{*}=x$.