Category:Self-Adjoint Densely-Defined Linear Operators

This category contains results about Self-Adjoint Densely-Defined Linear Operators.
Definitions specific to this category can be found in Definitions/Self-Adjoint Densely-Defined Linear Operators.

Let $\struct {\HH, \innerprod \cdot \cdot}$ be a Hilbert space.

Let $\struct {\map D T, T}$ be a densely defined linear operator on $\HH$

Let $\struct {\map D {T^\ast}, T^\ast}$ be the adjoint of $\struct {\map D T, T}$.

We say that $\struct {\map D T, T}$ is self-adjoint if and only if:

$\struct {\map D {T^\ast}, T^\ast} = \struct {\map D T, T}$