Subadditive measure on projectors of von neumann algebra
نویسندگان
چکیده
منابع مشابه
Von Neumann on Measure and Ergodic Theory
According to a currently popular principle of classification, mathematics is the study of various "categories. " A category consists of certain "objects" (e.g., groups, topological spaces) and certain "mappings" (e.g., homomorphisms, continuous functions). One possible category has measure spaces for its objects and, correspondingly, measure-preserving transformations for its mappings. The usua...
متن کاملVon 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...
متن کاملA Note on Faithful Traces on a Von Neumann Algebra
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; ...
متن کاملA Counterexample in Von Neumann Algebra Dynamics
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal on Integrated Education
سال: 2020
ISSN: 2620-3502,2615-3785
DOI: 10.31149/ijie.v3i1.262