The smooth entropy formalism for 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 ...

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.

Linear maps on von-Neumann algebras behaving like anti-derivations at orthogonal elements

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Strongly 1-bounded Von Neumann Algebras

Suppose F is a finite set of selfadjoint elements in a tracial von Neumann algebra M . For α > 0, F is α-bounded if Pα(F ) < ∞ where Pα is the α-packing entropy of F introduced in [7]. We say that M is strongly 1-bounded if M has a 1-bounded finite set of selfadjoint generators F such that there exists an x ∈ F with χ(x) > −∞. It is shown that if M is strongly 1-bounded, then any finite set of ...