On the automatic regularity of derivations from Riesz subalgebras of $\cal L^r(X)$

TL;DR

This paper studies the automatic regularity of bounded derivations from Banach lattice algebras of regular operators into compatible Banach modules, exploring conditions under which derivations exhibit regularity.

Contribution

It introduces conditions for the automatic regularity of derivations from Riesz subalgebras of operator algebras into Banach modules with lattice structures.

Findings

Identifies conditions ensuring derivations are regular

Establishes automatic regularity in specific algebraic contexts

Provides new insights into derivations in Banach lattice frameworks

Abstract

We investigate the automatic regularity of bounded derivations from a Banach lattice algebra of regular operators A into a Banach A-module with a Banach lattice structure compatible with the module operations.