$${\varvec{}}$$-Jorda homomorphisms ad pseudo $${\varvec{}}$$-Jorda homomorphisms o Baach algebras |
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Authors: | Ali?Ebadian Ali?Jabbari Email author" target="_blank">Nader?KanziEmail author |
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Institution: | 1.Department of Mathematics,Payame Noor University,Tehran,Iran |
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Abstract: | Let \(n\in \mathbb {N}\), A and B be Banach algebras and let B be a right A-module. We say that a linear mapping \(\varphi :A\longrightarrow B\) is a pseudo n-Jordan homomorphism if there exists an element \(w\in A\) such that \(\varphi (a^nw)=\varphi (a)^n\cdot w\), for every \(a\in A\) and \(n\ge \) 2. In this paper, among other things, we show that under some conditions if a linear mapping \(\varphi \) is a (pseudo) n-Jordan homomorphism, then it is a (pseudo) \((n + 1)\)-Jordan homomorphism. Additionally, we investigate automatic continuity of surjective pseudo n-Jordan homomorphisms under some conditions. |
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