Nondegenerate actions on Hilbert C*-modules

TL;DR

This paper investigates nondegenerate actions of C*-algebras on Hilbert C*-modules, establishing their equivalence and applying existing techniques to simplify proofs of recent related results.

Contribution

It proves the equivalence of two notions of nondegeneracy for C*-algebra actions on Hilbert modules and utilizes prior methods to streamline proofs of recent findings.

Findings

Proved the equivalence of two nondegeneracy notions

Applied Kim's techniques to simplify proofs

Connected actions on Hilbert modules with recent results

Abstract

Let X be a (right) Hilbert C*-module and let B be a C*-algebra acting on X from the left via adjointable operators. In this note we establish the equivalence of two notions of nondegeneracy for such an action of B on X. Furthermore, we explain how techniques from an earlier paper of Kim can be used to give a short proof of a recent result of Dessi, Kakariadis and Paraskevas.