Let A be (Figure presented.) unital prime Banach algebra over ℝ or ℂ with centre (Figure presented.) and G 1, G 2 be open subsets of (Figure presented.) be a continuous linear generalized skew derivation, and (Figure presented.) be a continuous linear map. We prove that (Figure presented.) 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 (Figure presented.). For each a ∈ G 1, b ∈ G 2, there exists an integer m ∈ Z >1 depending on a and b such that either (Figure presented.). 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]. © 2019 NISC (Pty) Ltd.

### On skew derivations and generalized skew derivations in Banach algebras

#### Abstract

Let A be (Figure presented.) unital prime Banach algebra over ℝ or ℂ with centre (Figure presented.) and G 1, G 2 be open subsets of (Figure presented.) be a continuous linear generalized skew derivation, and (Figure presented.) be a continuous linear map. We prove that (Figure presented.) 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 (Figure presented.). For each a ∈ G 1, b ∈ G 2, there exists an integer m ∈ Z >1 depending on a and b such that either (Figure presented.). 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]. © 2019 NISC (Pty) Ltd.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11570/3181481`