Suppose M is a tracial von Neumann algebra embeddable into R ω (the ultraproduct of the hyperfinite II 1-factor) and X is an n-tuple of selfadjoint generators for M. Denote by Γ(X; m, k, γ) the microstate space of X of order (m, k, γ). We say that X is tubular if for any ǫ > 0 there exist m ∈ N

The paper presents a fresh new comprehensive ideology on Neutrosophic Logic based on contradiction study in a broad sense: general critics on conventional logic by examining the essence of logic, fresh insights on logic definition based on Chinese philosophical survey, and a novel and genetic logic model as the elementary cell against Von Neumann oriented ones based on this novel definition. As...

We present a to following results in the constructive theory of operator algebras. A representation theorem for finite dimensional von Neumann-algebras. A representation theorem for normal functionals. The spectral measure is independent of the choice of the basis of the underlying Hilbert space. Finally, the double commutant theorem for finite von Neumann algebras and for Abelian von Neumann a...

Coset enumeration, based on the methods described by Todd and Coxeter, is one of the basic tools for investigating nitely presented groups. The process is not well understood, and various pathological presentations of, for example, the trivial group have been suggested as challenge problems. Here we consider one such family of presentations proposed by B.H. Neumann. We show that the problems ar...

Normal conditional expectations E : M → N ⊆ M of finite index on von Neumann algebras M with discrete center are investigated to find an estimate for the minimal number of generators of M as a Hilbert N-module. Analyzing the case of M being finite type I with discrete center we obtain that these von Neumann algebras M are always finitely generated projective N-modules with a minimal generator s...

In 1967, when Kadison and Ringrose began the development of continuous cohomology theory for operator algebras, they conjectured that the cohomology groups Hn(M, M), n >/= 1, for a von Neumann algebra M, should all be zero. This conjecture, which has important structural implications for von Neumann algebras, has been solved affirmatively in the type I, IIinfinity, and III cases, leaving open o...

Certain criteria are demonstrated for a spatial derivation of a von Neumann algebra to generate a one-parameter semigroup of endomorphisms of that algebra. These are then used to establish a converse to recent results of Borchers and of Wiesbrock on certain one-parameter semigroups of endomorphisms of von Neumann algebras (specifically, Type III1 factors) that appear as lightlike translations i...

Murray-von Neumann algebras are algebras of operators affiliated with finite von Neumann algebras. In this article, we study commutativity and affiliation of self-adjoint operators (possibly unbounded). We show that a maximal abelian self-adjoint subalgebra A of the Murray-von Neumann algebra A(f)(R) associated with a finite von Neumann algebra R is the Murray-von Neumann algebra A(f)(A(0)), wh...

We prove that it is not possible to classify separable von Neumann factors of types II1, II∞ or IIIλ, 0 ≤ λ ≤ 1, up to isomorphism by a Borel measurable assignment of “countable structures” as invariants. In particular the isomorphism relation of type II1 factors is not smooth. We also prove that the isomorphism relation for von Neumann II1 factors is analytic, but is not Borel.

Assume M is a type II1 von Neumann algebra, the algebra of n × n matrices over another von Neumann algebra N , with the tracial state τM. In this article, we discuss the properties of semicircular elements that are free with, with respect to τM, the algebra Dn consisting of scalar diagonal matrices in M. Then we define a concept “matricial distance” of two elements in M and compute it when the ...