Compact and "compact" operators on the standard Hilbert module over a $W^{\ast }$ algebra

Abstract

We construct a topology on the standard Hilbert module $l^2(\mathcal{A})$ over a unital $W^{\ast }$-algebra $\mathcal{A}$ such that any "compact" operator, (i.e.\ any operator in the norm closure of the linear span of the operators of the form $x\mapsto ⟨y,x⟩z$) maps bounded sets into totally bounded sets.

11 pages

Cited by in corpus (2)

• A Hilbert C*-module with extremal properties
• Topological and frame properties of certain pathological $C^{\ast }$-algebras