Research Article

On skew derivations and generalized skew derivations in Banach algebras

Published in: Quaestiones Mathematicae
Volume 43 , issue 9 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 1259–1272
DOI: 10.2989/16073606.2019.1607604
Author(s): Abdul Nadim Khan , Saudi Arabia, Shakir Ali , India, Husain Alhazmi , Saudi Arabia, Vincenzo De Filippis , Italy,
Keywords: 16W25, 46J10, 16W25, 46J10,
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Abstract

Let A be unital prime Banach algebra over ℝ or ℂ with centre and G 1, G 2 be open subsets of be a continuous linear generalized skew derivation, and be a continuous linear map. We prove that must be commutative if one of the following conditions holds:

For each a ∈ G 1 , b ∈ G 2, there exists an integer m ∈ Z >1 depending on a and b such that either .

For each a ∈ G 1 , b ∈ G 2, there exists an integer m ∈ Z >1 depending on a and b such that either .

 These results generalize a number of theorems of this type. In particular, as an application, we give an affirmative answer to some questions posed in [21].
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