The Dixmier approximation theorem in algebras of measurable operators

Quasi *-algebras of Measurable Operators

Non-commutative L-spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For p ≥ 2 they are also proved to possess a sufficient family of bounded positive sesquilinear forms satisfying certain invariance properties. CQ *-algebras of measurable operators over a finite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algeb...

Local Derivations on Algebras of Measurable Operators

The paper is devoted to local derivations on the algebra S(M, τ) of τ measurable operators affiliated with a von Neumann algebra M and a faithful normal semi-finite trace τ. We prove that every local derivation on S(M, τ) which is continuous in the measure topology, is in fact a derivation. In the particular case of type I von Neumann algebras they all are inner derivations. It is proved that f...

Dixmier Approximation and Symmetric Amenability for C ∗ - Algebras

We study some general properties of tracial C∗-algebras. In the first part, we consider Dixmier type approximation theorem and characterize symmetric amenability for C∗-algebras. In the second part, we consider continuous bundles of tracial von Neumann algebras and classify some of them.

Measurable Utility and the Measurable Choice Theorem

The Measurable Kesten Theorem

We give an explicit bound on the spectral radius in terms of the densities of short cycles in finite d-regular graphs. It follows that the a finite d-regular Ramanujan graph G contains a negligible number of cycles of size less than c log log |G|. We prove that infinite d-regular Ramanujan unimodular random graphs are trees. Through Benjamini-Schramm convergence this leads to the following rigi...