منابع مشابه
Von Neumann Algebra of Baumslag Group Embeds
In this paper we analyze the structure of some sets of non-commutative moments of elements in a finite von Neumann algebra M . If the fundamental group of M is R+\{0}, then the moment sets are convex, and if M is isomorphic to M ⊗M , then the sets are closed under pointwise multiplication. We introduce a class of discrete groups that we call hyperlinear. These are the discrete subgroups (with i...
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It is known that a semifinite von Neumann algebra always has a faithful semifinite trace. This trace can be used, for instance, to build up a non-commutative integration and, consequently, to define non commutative L-spaces. In this note we give some techniques for constructing, starting from a family F of semifinite traces, a faithful one which is closely related to the family F. Let F = {ηα; ...
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In this essay we construct a noncommutative von Neumann dynamical system with certain pathological properties from the viewpoint of analogies with classical ergodic theory. These relate to obstructions to the existence of special kinds of subsystem or subextension. We will build our example as an extension of a commutative dynamical system via a unitary cocycle acting on a Hilbert bundle, and w...
متن کاملOn a canonical lattice structure on the effect algebra of a von Neumann algebra
Let R be a von Neumann algebra acting on a Hilbert space H and let Rsa be the set of hermitean (i.e. selfadjoint) elements of R. It is well known that Rsa is a lattice with respect to the usual partial order ≤ if and only if R is abelian. We define and study a new partial order on Rsa, the spectral order ≤s, which extends ≤ on projections, is coarser than the usual one, but agrees with it on ab...
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Let M be a type I von Neumann algebra with the center Z and a faithful normal semi-finite trace τ. Let L(M, τ) be the algebra of all τ -measurable operators affiliated with M. We prove that any Z-linear derivation on L(M, τ) is inner and hence automatically continuous in the measure topology. If the lattice of projections from Z is atomic then any derivation on L(M, τ) is Z-linear. This implies...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1969
ISSN: 0040-8735
DOI: 10.2748/tmj/1178243042