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 self-adjoint or Hermitian :


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

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

Also see

 * Definition:Hermitian Matrix
 * Definition:Unitary Operator