Definition:Symmetric Densely-Defined Linear Operator

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

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

We say that $\struct {\map D T, T}$ is symmetric :


 * $\innerprod {T x} y = \innerprod x {T y}$ for all $x, y \in \map D T$.