A Hilbert \(C^*\)-module with extremal properties (Q2160243)
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| Language | Label | Description | Also known as |
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| English | A Hilbert \(C^*\)-module with extremal properties |
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A Hilbert \(C^*\)-module with extremal properties (English)
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3 August 2022
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It is shown that \textit{E. Troitsky}'s criterion of compactness for operators on Hilbert \(C^*\)-modules proved in [J. Math. Anal. Appl. 485, No. 2, Article ID 123842, 19 p. (2020; Zbl 1439.46046)] for countably generated Hilbert \(C^*\)-modules does not hold for certain uncountably generated modules. It is also shown that the module providing this counterexample does not admit frames.
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Hilbert \(C^*\)-module
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uniform structure
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totally bounded set
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compact operator
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\( {\mathcal A} \)-compact operator
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locally compact space
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Radon measure
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