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On skew derivations and generalized skew derivations in Banach algebras


Abdul Nadim Khan
Shakir Ali
Husain Alhazmi
Vincenzo De Filippis

Abstract

Let ? be a unital prime Banach algebra over ℝ or ℂ with centre tqma_a_1607604_ilg0002.gif and G1,G2 be open subsets of ?, F : ? → ? be a continuous linear generalized skew derivation, and D : ? → ? be a continuous linear map. We prove that ? must be commutative if one of the following conditions holds:
(a) For each a ∈ G1; b ∈ G2, there exists an integer m ∈ Z>1 depending on a and b
such that either tqma_a_1607604_ilg0006.gif.
(b) For each a ∈  G1; b ∈  G2, there exists an integer m ∈ Z >1 depending on a and b
such that either tqma_a_1607604_ilg0007.gif.
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].



Mathematics Subject Classication (2010): 16W25, 46J10.


Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606