Results 21 to 30 of about 601 (63)

A note on one‐parameter groups of automorphisms

International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 1, Page 135-138, 1990., 1988
Let {αt : t ∈ R} and {βt : t ∈ R} be two commuting one‐parameter groups of ∗‐automorphisms of a von Neumann algebra M such that αt + α−t = βt + β−t for all t ∈ R. The purpose of this note is to provide a simple and short proof of the central decomposition result: αt = βt on Mp and a αt = β−t on M(1 − p) for a central projection p ∈ M, without using the
A. B. Thaheem, Noor Mohammad
wiley   +1 more source

Pseudo-Diagonals and Uniqueness Theorems [PDF]

, 2013
We examine a certain type of abelian C*-subalgebra that allows one to give a unified treatment of two uniqueness theorems: for graph C*algebras and for certain reduced crossed products.
G. Nagy, Sarah Reznikoff
semanticscholar   +1 more source

On the operator equation α + α−1 = β + β−1

International Journal of Mathematics and Mathematical Sciences, Volume 9, Issue 4, Page 767-770, 1986., 1986
Let α, β be ∗‐automorphisms of a von Neumann algebra M satisfying the operator equation α + α−1 = β + β−1. In this paper we use new techniques (which are useful in noncommutative situations as well) to provide alternate proofs of the results:‐ If α, β commute then there is a central projection p in M such that α = β on MP and α = β−1 on M(1 − P); If M =
A. B. Thaheem
wiley   +1 more source

Classification of injective factors: The wok of Alain Connes

International Journal of Mathematics and Mathematical Sciences, Volume 6, Issue 1, Page 1-39, 1983., 1983
The fundamental results of A. Connes which determine a complete set of isomorphism classes for most injective factors are discussed in detail. After some introductory remarks which lay the foundation for the subsequent discussion, an historical survey of some of the principal lines of the investigation in the classification of factors is presented ...
Steve Wright
wiley   +1 more source

Uniqueness questions for C*-norms on group rings

, 2018
We provide a large class of discrete amenable groups for which the complex group ring has several C*-completions, thus providing partial evidence towards a positive answer to a question raised by Rostislav Grigorchuk, Magdalena Musat and Mikael R{\o}rdam.
Alekseev, Vadim, Kyed, David
core   +1 more source

On the range of completely bounded maps

International Journal of Mathematics and Mathematical Sciences, Volume 1, Issue 2, Page 209-215, 1978., 1978
It is shown that if every bounded linear map from a C*‐algebra α to a von Neumann algebra β is completely bounded, then either α is finite‐dimensional or β⫅𝒞 ⊗ Mn, where 𝒞 is a commutative von Neumann algebra and Mn is the algebra of n × n complex matrices.
Richard I. Loebl
wiley   +1 more source

On the first continuous $L^2$-cohomology of free group factors

, 2014
We prove that the first continuous $L^2$-cohomology of free group factors vanishes. This answers a question by Andreas Thom regarding continuity properties of free difference quotients and shows that one can not distinguish free group factors by means of
Alekseev, Vadim
core   +1 more source

Weak asymptotic homomorphism property for masas in semifinite factors

, 2013
The notion of weak asymptotic homomorphism property for masas in semifinite factors is defined and is shown to be equivalent to singularity. The analysis shows that weak asymptotic homomorphism property is a ‘spectral phenomenon’.
Kunal Mukherjee
semanticscholar   +1 more source

Elementary equivalence and disintegration of tracial von Neumann algebras

Forum of Mathematics, Sigma
We prove an analog of the disintegration theorem for tracial von Neumann algebras in the setting of elementary equivalence rather than isomorphism, showing that elementary equivalence of two direct integrals of tracial factors implies fiberwise ...
David Gao, David Jekel
doaj   +1 more source

Complex Hadamard matrices and Equiangular Tight Frames [PDF]

, 2011
In this paper we give a new construction of parametric families of complex Hadamard matrices of square orders, and connect them to equiangular tight frames. The results presented here generalize some of the recent ideas of Bodmann et al.
Szöllősi, Ferenc
core