Operator predual from matrix coefficients
= Operator predual from matrix coefficients
For a <Hilbert space> $H$, the linear span of the matrix-coefficient functionals $T\mapsto\langle Tx,y\rangle$ is a predual of $\mathcal B(H)$. The unit ball is compact in the resulting <weak operator topology> by the <Tychonoff theorem>, and the <compact norming dual-pair criterion> identifies $\mathcal B(H)$ with the dual of that span.