Spaces of continuous sesquilinear forms associated with unbounded operator algebras (Q1122126)

Summary: Let \({\mathcal A}\) be a closed *-algebra of unbounded operators on a dense invariant domain \({\mathcal D}\) of a Hilbert space, and let \({\mathcal L}_{{\mathcal A}}({\mathcal D},{\mathcal D}')\) be the vector space of all continuous sesquilinear forms on \({\mathcal D}\times {\mathcal D}\) relative to the graph topology of \({\mathcal A}\). We generalize some basic results of the von Neumann algebra theory (von Neumann bicommutant theorem, Kaplansky density theorem) to certain linear subspaces of \({\mathcal L}_{{\mathcal A}}({\mathcal D},{\mathcal D}')\).