David P. Blecher
Metric characterizations II.
Tue, 02/28/2012 - 15:01 — SomNambulAuthors: David P. Blecher, Matthew Neal
Subjects: Operator Algebras
AbstractThe present paper is a sequel to our paper "Metric characterization of
isometries and of unital operator spaces and systems". We characterize certain
common objects in the theory of operator spaces (unitaries, unital operator
spaces, operator systems, operator algebras, and so on), in terms which are
purely linear-metric, by which we mean that they only use the vector space
structure of the space and its matrix norms. In the last part we give some
characterizations of operator algebras (which are not linear-metric in our
strict sense described in the paper).A characterization and a generalization of W*-modules.
Mon, 08/31/2009 - 17:16 — SomNambulAuthors: David P. Blecher, Upasana Kashyap
Subjects: Operator Algebras
AbstractWe 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 $\sigma$-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.
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