Commutativity of Banach algebras involving endomorphisms
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Mohammadi El Hamdaoui
Abstract
In this article, we present new contributions to the study of endomorphisms within algebraic structures, particularly focusing on prime Banach algebras. We establish that any prime Banach algebra must be commutative if it admits endomorphisms and multipliers satisfying specific algebraic identities. Our main results generalize several known theorems. Additionally, we provide an illustrative example demonstrating that the primeness assumption in several theorems is indeed essential.
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