Self-adjoint

Self-adjoint

In mathematics, an element x of a star-algebra is self-adjoint if the involution acts trivially upon it. In other words, . When we work in an inner product space which is a star-algebra, being self-adjoint is the same as being hermitian.

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