October 8, 2025Open Access

Nondegenerate actions on Hilbert C*-modules

EKElias G. KatsoulisEast Carolina University CRChristopher Bronk RamseyUniversity of Oxford

Puntos clave

Two notions of nondegeneracy for the action of a C*-algebra on a Hilbert C*-module are shown to be equivalent.
Using techniques from a previous work by Kim, a concise proof of a result by Dessi, Kakariadis, and Paraskevas is provided.
The equivalence discussed applies specifically to adjointable operators acting on Hilbert C*-modules.
Insights gained could further develop the understanding of operator actions in mathematical frameworks.

Resumen

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.

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Cite This Study

Katsoulis et al. (Wed,) studied this question.

synapsesocial.com/papers/68e6494525bc5bdb98713bf8 https://doi.org/https://doi.org/10.48550/arxiv.2507.17104