May 8, 2024Open Access

A separation theorem for Hilbert W^*-modules

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Abstract

Let L be a closed submodule of a Hilbert W^*-module E over a C^*-algebra A. We pose a separation problem: Does there exist a normal state such that _ (L) is not dense in E_? In this note, among other results, we give an affirmative answer to this problem, when E is a self-dual Hilbert W^*-module such that E L has a nonempty interior with respect to the weak^*-topology.

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

synapsesocial.com/papers/68e6b14fb6db6435876332a7 https://doi.org/https://doi.org/10.48550/arxiv.2405.04850

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