Self-Duality and $C\ast$-Reflexivity of Hilbert $C\ast$-Moduli

Abstract

The subjects of this paper are a new definition of the notion "self-dual Hilbert $C\ast$-module" as a- categorical concept of Banach $C\ast$-moduli, and the conditions for some Hilbert $C\ast -modulitobeself-dualor$ C*$-reflexive.TheisomorphismofanytwoHilbertstructuresonagivenself-dualHilbert$ C*$-moduleinducingequivalentnormstothegivenoneisstated.Atopologicalcriterionofself-dualityand$ C*$reflexivityofHilbert$ W*$-moduIiisproved.Acriterionofself-dualityofthecountablygeneratedHilbert$ \mathcal A$-module$ l_2(\mathcal A) $isstatedforarbitrary$ C*$-algebras$ \mathcal A$. As an application the classification of countably generated Hilbert W*modimli by their structure is given.