Derivations of von Neumann algebras into the compact ideal space of a semifinite algebra

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.

Derivations on the Algebra of τ-Compact Operators Affiliated with a Type I von Neumann Algebra

Let M be a type I von Neumann algebra with the center Z, a faithful normal semi-finite trace τ. Let L(M, τ) be the algebra of all τ -measurable operators affiliated with M and let S0(M, τ) be the subalgebra in L(M, τ) consisting of all operators x such that given any ε > 0 there is a projection p ∈ P(M) with τ(p) < ∞, xp ∈ M and ‖xp‖ < ε. We prove that any Z-linear derivation of S0(M, τ) is spa...

the structure of lie derivations on c*-algebras

نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.

Triple Derivations on Von Neumann Algebras

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 pr...

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