@article{Ali2024, 
author = {Shakir Ali and Ali Yahya Hummdi and Mohammed Ayedh and Naira Noor Rafiquee},
title = {Linear generalized derivations on Banach  ∗-algebras},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {10},
pages = {27497-27511},
keywords = {Banach ∗-algebra, linear derivation, linear generalized derivation, involution},
url = {https://www.sciopen.com/article/10.3934/math.20241335},
doi = {10.3934/math.20241335},
abstract = {This paper deals with some identities on Banach  ∗-algebras that are equipped with linear generalized derivations. As an application of one of our results, we describe the structure of the underlying algebras. Precisely, we prove that for a linear generalized derivation  F on a Banach  ∗-algebra  A, either we obtain the existence of a central idempotent element  e∈Q, for which  F=0 on  eQ and  (1−e)Q satisfies  s4, or the set of elements  u∈A such that the identity  [F(u)n,F(u∗)nF(u)n]∈Z(A) holds for no positive integer  n turns out to be dense. In addition to this we consider an identity satisfied by a semisimple Banach  ∗-algebra and look for its commutativity. Moreover, some related results are also established.}
}