Generalized derivations and commutativity of prime Banach algebras

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• 作者：R. K. Sharma ; B. Prajapati
• 关键词：Prime Banach algebra ; Generalized derivation ; Left multiplier
• 刊名：Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：58
• 期：1
• 页码：179-187
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algebra; Geometry; Algebraic Geometry; Convex and Discrete Geometry;
• 出版者：Springer Berlin Heidelberg
• ISSN：2191-0383
• 卷排序：58

文摘

In this article we study various conditions on a unital prime Banach algebra that ensure its commutativity. More specifically, we prove that a unital prime Banach algebra A with a nonzero continuous linear generalized derivation g associated with a nonzero linear continuous derivation d satisfying either \(g((xy)^n)-d(x^n)d(y^n)\in Z(A)\) or \(g((xy)^n)-d(y^n)d(x^n)\in Z(A)\), for sufficiently many x, y and an integer \(n=n(x,y)>1\) is commutative.