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ISSN 1088-6850(e) ISSN 0002-9947(p)

A characterization and a generalization of -modules

Author(s): David P. Blecher; Upasana Kashyap
Journal: Trans. Amer. Math. Soc. 363 (2011), 345-363.
MSC (2010): Primary 46L08, 47L30, 47L45; Secondary 16D90, 47L25
Posted: August 18, 2010
MathSciNet review: 2719685
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We give a new Banach module characterization of -modules, also known as self-dual Hilbert -modules over a von Neumann algebra. This leads to a generalization of the notion, and the theory, of -modules, to the setting where the operator algebras are $\sigma$ -weakly closed algebras of operators on a Hilbert space. That is, we find the appropriate weak* topology variant of our earlier notion of rigged modules, and their theory, which in turn generalizes the notions of a -module and a Hilbert space, successively. Our -rigged modules have canonical `envelopes' which are -modules. Indeed, a -rigged module may be defined to be a subspace of a -module possessing certain properties.

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