Some differential identities on prime Banach algebras

Abstract

In this paper, we investigate the commutativity of a Banach algebra [Formula: see text] provided with a continuous derivation satisfying algebraic identities involving nonvoid open subsets of [Formula: see text] Furthermore, we provide examples to show that various restrictions in the hypothesis of our theorems are not superfluous.

Commutativity Theorems and Projection on the Center of a Banach Algebra

“…Numerous results in the literature concerning the commutativity of a prime and semi-prime Banach algebra are proved, for example, in 2022, M. Moumen, L. Taoufiq and L. Oukhtite [5] showed that if X is a prime Banach algebra having two non-void open subsets H 1 and H 2 such that for all (x, y)…”