Compact and "Compact" operators on standard Hilbert modules over C*-algebras

Abstract

We construct a topology on the standard Hilbert module H<inf>A</inf> over a unital C*-algebra and topology on H<inf>A</inf> ^# (the extension of the module H<inf>A</inf> by the algebra A* *) such that any "compact" operator (i.e. any operator in the norm closure of the linear span of the operators of the form z x 〈y; z〉, x,y ∈ H<inf>A</inf> (or x,y ∈ H<inf>A</inf> ^#)) maps bounded sets into totally bounded sets.