On von Neumann Algebras Which Are Complemented Subspaces of B(H)

Remarks on Complemented Subspaces of Von-neumann Algebras*

In this note we include two remarks about bounded (not necessarily contractive) linear projections on a von Neumann-algebra. We show that if M is a von Neumann-subalgebra of B(H) which is complemented in B(H) and isomorphic to M ⊗ M then M is injective (or equivalently M is contractively complemented). We do not know how to get rid of the second assumption on M. In the second part,we show that ...

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.

On Some Free Products of Von Neumann Algebras Which Are Free Araki-woods Factors

We prove that certain free products of factors of type I and other von Neumann algebras with respect to nontracial, almost periodic states are almost periodic free Araki-Woods factors. In particular, they have the free absorption property and Connes’ Sd invariant completely classifies these free products. For example, for λ, μ ∈]0, 1[, we show that (M2(C), ωλ) ∗ (M2(C), ωμ) is isomorphic to the...

Notes on 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 ...