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

Michael Frank

doi:10.4171/zaa/390

JournalszaaVol. 9, No. 2pp. 165–176

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

Michael Frank
Hochschule für Technik, Wirtschaft und Kultur, Leipzig, Germany

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Abstract

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 $C * - m o d u l i t o b ese l f - d u a l or$ C* $- re f l e x i v e . T h e i so m or p hi s m o f an y tw oH i l b er t s t r u c t u reso na g i v e n se l f - d u a l H i l b er t$ C* $- m o d u l e in d u c in g e q u i v a l e n t n or m s t o t h e g i v e n o n e i ss t a t e d . A t o p o l o g i c a l cr i t er i o n o f se l f - d u a l i t y an d$ C* $re f l e x i v i t yo f H i l b er t$ W* $- m o d u I ii s p ro v e d . A cr i t er i o n o f se l f - d u a l i t yo f t h eco u n t ab l y g e n er a t e d H i l b er t$ \mathcal A $- m o d u l e$ l_2(\mathcal A) $i ss t a t e df or a r bi t r a ry$ C* $- a l g e b r a s$ \mathcal A$. As an application the classification of countably generated Hilbert W*modimli by their structure is given.

Cite this article

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

DOI 10.4171/ZAA/390