Derivations with values in quasi-normed bimodules of locally measurable operators

TL;DR

This paper proves that all derivations from a von Neumann algebra into a quasi-normed bimodule of locally measurable operators are inner, extending understanding of derivation structures in operator algebras.

Contribution

It establishes that any derivation into a quasi-normed bimodule of locally measurable operators is necessarily inner, a significant generalization in the theory of operator algebras.

Findings

All derivations are inner.

Extension to quasi-normed bimodules of locally measurable operators.

Advances the understanding of derivation structures in von Neumann algebras.

Abstract

We prove that every derivation acting on a von Neumann algebra $\mathcal{M}$ with values in a quasi-normed bimodule of locally measurable operators affiliated with $\mathcal{M}$ is necessarily inner.