2007/12/09 by Blecher, David P., Kashyap, Upasana
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.0712.1236
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 \em rigged modules, and their theory, which in turn generalizes the notions of C*-module, and Hilbert space, successively. Our \em 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.