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Stability of the Jensen-type functional equation in $C^{*}$ -algebras: a fixed point approach.

Park, Choonkil, Rassias, John Michael (2009)

Abstract and Applied Analysis

Stochastic Dynamics of Quantum Spin Systems

Adam Majewski, Robert Olkiewicz, Bogusław Zegarliński (1998)

Banach Center Publications

We show that recently introduced noncommutative $L_{p}$ -spaces can be used to constructions of Markov semigroups for quantum systems on a lattice.

Strong mixing Markov semigroups on C₁ are meager

Wojciech Bartoszek, Beata Kuna (2006)

Colloquium Mathematicae

We show that the set of those Markov semigroups on the Schatten class ₁ such that in the strong operator topology $l i m_{t \to \infty} T (t) = Q$ , where Q is a one-dimensional projection, form a meager subset of all Markov semigroups.

Subproduct systems.

Shalit, Orr, Solel, Baruch (2009)

Documenta Mathematica

The variational approach to the Dirichlet problem in C*-algebras

Fabio Cipriani (1998)

Banach Center Publications

The aim of this work is to develop the variational approach to the Dirichlet problem for generators of sub-Markovian semigroups on C*-algebras. KMS symmetry and the KMS condition allow the introduction of the notion of weak solution of the Dirichlet problem. We will then show that a unique weak solution always exists and that a generalized maximum principle holds true.

Topologies on central extensions of von Neumann algebras

Shavkat Ayupov, Karimbergen Kudaybergenov, Rauaj Djumamuratov (2012)

Open Mathematics

Given a von Neumann algebra M, we consider the central extension E(M) of M. We introduce the topology t c(M) on E(M) generated by a center-valued norm and prove that it coincides with the topology of local convergence in measure on E(M) if and only if M does not have direct summands of type II. We also show that t c(M) restricted to the set E(M)h of self-adjoint elements of E(M) coincides with the order topology on E(M)h if and only if M is a σ-finite type Ifin von Neumann algebra.

Triple derivations on von Neumann algebras

Robert Pluta, Bernard Russo (2015)

Studia Mathematica

It is well known that every derivation of a von Neumann algebra into itself is an inner derivation and that every derivation of a von Neumann algebra into its predual is inner. It is less well known that every triple derivation (defined below) of a von Neumann algebra into itself is an inner triple derivation. We examine to what extent all triple derivations of a von Neumann algebra into its predual are inner. This rarely happens but it comes close. We prove a (triple) cohomological...