Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 308
Commutativity Of Banach Algebras And Differential Identities
Mohamed Moumen, Lahcen Taoufiq
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 30, 2022
March 03, 2267
April 15, 2267

Abstract: Let B be a Banach algebra with center Z(B). Our aim through this paper is to study the commutativity of B if some specific algebraic identities on non-empty open subsets of B are holds. Our topological approach is based on Baire's category theorem and some properties of functional analysis. Among our results, we have proved that a prime Banach algebra B must be commutative if there are non-empty open subsets H_1 and H_2of B such that for all (x,y)∈H_1×H_2 there are strictly positive integers n,m such that x^n oy^m∈ Z(B). Furthermore, we include some examples to show that various ...