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arXiv · 2406.17701

Jordan and Lie derivations of $ϕ$-Johnson amenable Banach algebras

Hoger Ghahramani·Parvin Zamani
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Abstract

Let U be a $ϕ$-Johnson amenable Banach algebra in which $ϕ$ is a non-zero multiplicative linear functional on U. Suppose that X is a Banach U-bimodule such that $a.x=ϕ(a)x$ for all a in U and x in X or $x.a=ϕ(a)x$ for all a in U and x in X. We show that every continuous Jordan derivation from U to X is a derivation, and every continuous Lie derivation from U to X decomposed into the sum of a continuous derivation and a continuous center-valued trace.

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Hoger Ghahramani, Parvin Zamani. 2024-06-25. Jordan and Lie derivations of $ϕ$-Johnson amenable Banach algebras. https://doi.org/10.1142/s0219498825503475

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