Strong commutativity preserving skew derivations on Banach algebras

Abstract

A map $ \delta : \mathcal {S}\subseteq \mathcal {A} \rightarrow \mathcal {A} $ is called a strong commutativity preserving (SCP) on $ \mathcal {S} $ if $ [\delta (x),\delta (y)]=[x, y] $ for all $ x, y \in \mathcal {S} $ , where $ \mathcal {A} $ is a Banach algebra over $ \mathbb {C} $ or $ \mathbb {R} $ and $ \mathcal {S} $ is a nonempty subset of $ \mathcal {A} $ . The main goal of this manuscript is to investigate the SCP skew derivations on Banach algebra $ \mathcal {A} $ and we obtain action of skew derivations on rings and the structure of prime Banach algebras.

Keywords

• prime banach algebra
• strong commutativity preserving (scp) map
• skew derivation