Complete Ccc Boolean Algebras, the Order Sequential Topology, and a Problem of Von Neumann

Complete Ccc Boolean Algebras

Let B be a complete ccc Boolean algebra and let τs be the topology on B induced by the algebraic convergence of sequences in B. 1. Either there exists a Maharam submeasure on B or every nonempty open set in (B, τs) is topologically dense. 2. It is consistent that every weakly distributive complete ccc Boolean algebra carries a strictly positive Maharam submeasure. 3. The topological space (B, τ...

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 ...

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.

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

Von Neumann’s Problem and Large Cardinals

It is a well known problem of Von Neumann whether the countable chain condition and weak distributivity of a complete Boolean algebra imply that it carries a strictly positive probability measure. It was shown recently by Balcar–Jech–Pazák and Velickovic that it is consistent with ZFC, modulo the consistency of a supercompact cardinal, that every ccc weakly distributive complete Boolean algebra...