Selfadjoint

In mathematics, an element x of a *-algebra is self-adjoint if ${\displaystyle x^{*}=x}$.

A collection C of elements of a star-algebra is self-adjoint if it is closed under the involution operation. For example, if ${\displaystyle x^{*}=y}$ then since ${\displaystyle y^{*}=x^{**}=x}$ in a star-algebra, the set {x,y} is a self-adjoint set even though x and y need not be self-adjoint elements.

...
Wikipedia