Embedding Dimensions of Finite 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 ...

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

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.

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

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On a Reduction Procedure for Horn Inequalities in Finite Von Neumann Algebras

We consider the analogues of the Horn inequalities in finite von Neumann algebras, which concern the possible spectral distributions of sums a + b of self–adjoint elements a and b in a finite von Neumann algebra. It is an open question whether all of these Horn inequalities must hold in all finite von Neumann algebras, and this is related to Connes’ embedding problem. For each choice of integer...