Fractal Dimensions and Von Neumann Algebras

Various topological forms of Von Neumann regularity in Banach algebras

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

Nonlinear $*$-Lie higher derivations on factor von Neumann algebras

Let $mathcal M$ be a factor von Neumann algebra. It is shown that every nonlinear $*$-Lie higher derivation$D={phi_{n}}_{ninmathbb{N}}$ on $mathcal M$ is additive. In particular, if $mathcal M$ is infinite type $I$factor, a concrete characterization of $D$ is given.

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Linear maps on von-Neumann algebras behaving like anti-derivations at orthogonal elements

This article has no abstract.

Embedding Dimensions of Finite von Neumann Algebras

We introduce “embedding dimensions” of a family of generators of a finite von Neumann algebra when the von Neumann algebra can be faithfully embedded into the ultrapower of the hyperfinite II1 factor. These embedding dimensions are von Neumann algebra invariants, i.e., do not depend on the choices of the generators. We also find values of these invariants for some specific von Neumann algebras.