Jordan *-derivation pairs on a complex *-algebra
type: Item
instance of: scholarly article
title: Jordan *-derivation pairs on a complex *-algebra
zbMATH Open document ID: 0887.16021
DOI: 10.1007/BF02755445
published in: Aequationes Mathematicae
publication date: 1998-05-25T00:00:00Z
full work available at URL: https://eudml.org/doc/137693
review text: Let \(A\) be a ring with involution * and \(M\) be an \(A\)-bimodule. The paper considers pair of functions \(E,F\colon A\to M\) satisfying \(E(x^3)=E(X)x^{*^2}+xF(x)x^*+x^2E(x)\) and \(F(x^3)=F(X)x^{*^2}+xE(x)x^*+x^2F(x)\) for all \(x\in A\), and thereby extends the treatment of the so-called Jordan *-derivation pairs introduced by \textit{B. Zalar} [Aequationes Math. 54, No. 1-2, 31-43 (1997; Zbl 0881.39019)]. The main result asserts that if \(A\) is a complex algebra and \(M\) has the property that \(A^2f=0\) of \(fA^2=0\), where \(f\in M\), implies \(f=0\), then \(E\) and \(F\) are of the form \(E(x)=T_1(x^*)+S_2(x)\), \(F(x)=-(T_2(x^*)+S_1(x))\), where \((T_1,S_1)\) and \((T_2,S_2)\) are double centralizers of \(A\) into \(M\).
Mathematics Subject Classification ID: 16W10
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 47B47
zbMATH DE Number: 1053598
zbMATH Keywords: rings with involutions
zbMATH Keywords: Jordan *-derivation pairs
zbMATH Keywords: complex algebras
zbMATH Keywords: double centralizers
author: Lajos Molnár
reviewed by: Matej Brešar
MaRDI profile type: Publication
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OpenAlex ID: W4250134262
description: scientific article; zbMATH DE number 1053598