Stone Spectra of 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 ...

0 60 50 20 v 1 5 M ay 2 00 6 Stone spectra of finite von Neumann algebras of type I n Hans

In this paper, we clarify the structure of the Stone spectrum of an arbitrary finite von Neumann algebra R of type In. The main tool for this investigation is a generalized notion of rank for projections in von Neumann algebras of this type.

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

ar X iv : m at h - ph / 0 50 90 20 v 1 1 1 Se p 20 05 Observables I : Stone Spectra

In this work we discuss the notion of observable both quantum and classical from a new point of view. In classical mechanics, an observable is represented as a function (measurable, continuous or smooth), whereas in (von Neumann’s approach to) quantum physics, an observable is represented as a bonded selfadjoint operator on Hilbert space. We will show in part II of this work that there is a com...

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.