A Remark on the structure of symmetric quantum dynamical semigroups on von Neumann algebras

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.

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 ...

Ergodic Property of Markovian Semigroups on Standard Forms of von Neumann Algebras

We give sufficient conditions for ergodicity of the Markovian semigroups associated to Dirichlet forms on standard forms of von Neumann algebras constructed by the method proposed in Refs.[Par1, Par2]. We apply our result to show that the diffusion type Markovian semigroups for quantum spin systems are ergodic in the region of high temperatures where the uniqueness of the KMS-state holds.

E0-semigroups in Quantum Field Theory

A lecture presented at the von Neumann symposium on Quantization and Nonlinear Wave Equations held at MIT in June, 1994. We describe the role of semigroups of endomorphisms of von Neumann algebras in algebraic formulations of quantum field theory, and present a summary of recent developments in the theory of E0-semigroups. 1991 Mathematics Subject Classification. Primary 46L40; Secondary 81E05.