Algebras of multiplicators and spaces of quasimultiplicators (Q1406442)

Basic results of the paper are contained in the following two assertions. For any Hilbert module \({\mathcal E}\) the isomorphism of the Banach spaces \(\text{Hom}_\Lambda({\mathcal E},{\mathcal E}')\cong {\mathcal Q}{\mathcal M}({\mathcal K}({\mathcal E}))\) holds true, where \({\mathcal K}({\mathcal E})\) denotes the \(C^*\)-algebra of compact operators in \({\mathcal E}\). For any Hilbert module \({\mathcal E}\), the isomorphism of Banach algebras \(\text{End}_{\Lambda}({\mathcal E},{\mathcal E}')\cong LM({\mathcal K}({\mathcal E}))\) holds true.