A Hilbert C*-module with extremal properties

Abstract

We construct an example of a Hilbert C*-module which shows that Troitsky's theorem on the geometrical essence of A-compact operators between Hilbert C*-modules is not extendable to a not countably generated module case (even in the case of a stronger uniform structure, which is also introduced). In addition, the constructed module admits no frames.

In Russian

Cited by in corpus (1)

• Topological and frame properties of certain pathological $C^{\ast }$-algebras