Definition:Hermitian Operator

Definition
Let $\HH$ be a Hilbert space.

Let $\mathbf T: \HH \to \HH$ be a bounded linear operator.

Then $\mathbf T$ is said to be Hermitian :


 * $\mathbf T = \mathbf T^*$

That is, it equals its adjoint $\mathbf T^*$.

Also known as
A Hermitian operator is also known as a self-adjoint operator.

Also see

 * Definition:Hermitian Matrix
 * Definition:Unitary Operator
 * Definition:Self-Adjoint Densely-Defined Linear Operator