Unbounded derivations and *-automorphisms groups of Banach quasi *-algebras

TL;DR

This paper investigates unbounded derivations on Banach quasi *-algebras, focusing on their role as generators of automorphism groups using weak formulations, and provides conditions for such derivations to generate automorphisms.

Contribution

It introduces conditions under which weak *-derivations on Banach quasi *-algebras generate automorphism groups, extending the understanding of their infinitesimal structure.

Findings

Conditions for weak *-derivations to generate automorphism groups are established.

The study emphasizes the use of bounded sesquilinear forms in the analysis.

It advances the theory of unbounded derivations in the context of Banach quasi *-algebras.

Abstract

This paper is devoted to the study of unbounded derivations on Banach quasi *-algebras with a particular emphasis to the case when they are infinitesimal generators of one parameter automorphisms groups. Both of them, derivations and automorphisms are considered in a weak sense; i.e., with the use of a certain families of bounded sesquilinear forms. Conditions for a weak *-derivation to be the generator of a *-automorphisms group are given.