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Derivable maps at commutative products on Banach algebras

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Abstract

Let A be a unital Banach algebra with unit e, M be a Banach A-bimodule, and \(w\in A\). In this paper, we characterize those continuous linear maps \(\delta :A\rightarrow M\) that satisfy one of the following conditions:

$$\begin{aligned} \delta (ab)= & {} \delta (a)b+a\delta (b), \\ 2\delta (w)= & {} \delta (a)b+a\delta (b),\\ \delta (ab)= & {} \delta (a)b+a\delta (b)-a\delta (e)b, \end{aligned}$$

for any \(a,b\in A\) with \(ab=ba=w\), where w is either a separating point with \(w\in Z(A)\) or an idempotent.

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Acknowledgements

The authors gratefully acknowledge for careful reading of the manuscript and for helpful comments of the anonymous referees.

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Correspondence to Abbas Zivari-Kazempour.

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Zivari-Kazempour, A., Ghahramani, H. Derivable maps at commutative products on Banach algebras. Acta Sci. Math. (Szeged) 90, 165–174 (2024). https://doi.org/10.1007/s44146-023-00104-8

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