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Zeitschrift für Analysis und ihre Anwendungen


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Volume 9, Issue 2, 1990, pp. 165–176
DOI: 10.4171/ZAA/390

Published online: 1990-04-30

Self-Duality and $C*$-Reflexivity of Hilbert $C*$-Moduli

Michael Frank[1]

(1) Hochschule für Technik, Wirtschaft und Kultur, Leipzig, Germany

The subjects of this paper are a new definition of the notion "self-dual Hilbert $C*$-module" as a- categorical concept of Banach $C*$-moduli, and the conditions for some Hilbert $C*-moduli to be self-dual or $C*$-reflexive. The isomorphism of any two Hilbert structures on a given self-dual Hilbert $C*$-module inducing equivalent norms to the given one is stated. A topological criterion of self-duality and $C*$reflexivity of Hilbert $W*$-moduIi is proved. A criterion of self-duality of the countably generated Hilbert $\mathcal A$-module $l_2(\mathcal A)$ is stated for arbitrary $C*$-algebras $\mathcal A$. As an application the classification of countably generated Hilbert W*modimli by their structure is given.

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Frank Michael: Self-Duality and $C*$-Reflexivity of Hilbert $C*$-Moduli. Z. Anal. Anwend. 9 (1990), 165-176. doi: 10.4171/ZAA/390