ar X iv : 0 71 2 . 12 36 v 2 [ m at h . O A ] 2 7 A ug 2 00 9 A CHARACTERIZATION AND A GENERALIZATION OF W ∗ - MODULES
نویسندگان
چکیده
We give a new Banach module characterization of W *-modules, also known as selfdual Hilbert C *-modules over a von Neumann algebra. This leads to a generalization of the notion, and the theory, of W *-modules, to the setting where the operator algebras are σ-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 C *-module, and Hilbert space, successively. Our w *-rigged modules have canonical 'envelopes' which are W *-modules. Indeed, w *-rigged modules may be defined to be a subspace of a W *-module possessing certain properties.
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