منابع مشابه
Hilbert modules and modules over finite von Neumann algebras and applications to L2-invariants
Throughout this paper A is a finite von Neumann algebra and tr :A −→ C is a finite normal faithful trace. Recall that a von Neumann algebra is finite if and only if it possesses such a trace. Let l2(A) be the Hilbert space completion of A which is viewed as a pre-Hilbert space by the inner product 〈a, b〉 = tr(ab∗). A finitely generated Hilbert A-module V is a Hilbert space V together with a lef...
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We review some of our results from the theory of product systems of Hilbert modules [BS00, BBLS00, Ske00a, Ske01, Ske02, Ske03]. We explain that the product systems obtained from a CP-semigroup in [BS00] and in [MS02] are commutants of each other. Then we use this new commutant technique to construct product systems from E0–semigroups on Ba(E) where E is a strongly full von Neumann module. (Thi...
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We show that each R-module is n-flat (resp., weakly n-flat) if and only if R is an (n,n− 1)-ring (resp., a weakly (n,n− 1)-ring). We also give a new characterization of n-von Neumann regular rings and a characterization of weak n-von Neumann regular rings for (CH)-rings and for local rings. Finally, we show that in a class of principal rings and a class of local Gaussian rings, a weak n-von Neu...
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We give an overview of relative tensor products (RTPs) for von Neumann algebra modules. For background, we start with the categorical definition and go on to examine its algebraic formulation, which is applied to Morita equivalence and index. Then we consider the analytic construction, with particular emphasis on explaining why the RTP is not generally defined for every pair of vectors. We also...
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ژورنال
عنوان ژورنال: Communications on Stochastic Analysis
سال: 2012
ISSN: 0973-9599
DOI: 10.31390/cosa.6.1.05