JournalszaaVol. 9, No. 2pp. 165–176

Self-Duality and CC*-Reflexivity of Hilbert CC*-Moduli

  • Michael Frank

    Hochschule für Technik, Wirtschaft und Kultur, Leipzig, Germany
Self-Duality and $C*$-Reflexivity of Hilbert $C*$-Moduli cover
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The subjects of this paper are a new definition of the notion "self-dual Hilbert CC*-module" as a- categorical concept of Banach CC*-moduli, and the conditions for some Hilbert CmodulitobeselfdualorC*-moduli to be self-dual or C*reflexive.TheisomorphismofanytwoHilbertstructuresonagivenselfdualHilbert-reflexive. The isomorphism of any two Hilbert structures on a given self-dual Hilbert C*moduleinducingequivalentnormstothegivenoneisstated.Atopologicalcriterionofselfdualityand-module inducing equivalent norms to the given one is stated. A topological criterion of self-duality and C*reflexivityofHilbertreflexivity of Hilbert W*moduIiisproved.AcriterionofselfdualityofthecountablygeneratedHilbert-moduIi is proved. A criterion of self-duality of the countably generated Hilbert \mathcal Amodule-module l_2(\mathcal A) isstatedforarbitraryis stated for arbitrary C*algebras-algebras \mathcal A$. As an application the classification of countably generated Hilbert W*modimli by their structure is given.

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Michael Frank, Self-Duality and CC*-Reflexivity of Hilbert CC*-Moduli. Z. Anal. Anwend. 9 (1990), no. 2, pp. 165–176

DOI 10.4171/ZAA/390