Jordan *-derivation pairs and quadratic functionals on modules over *-rings
type: Item
instance of: scholarly article
title: Jordan *-derivation pairs and quadratic functionals on modules over *-rings
zbMATH Open document ID: 0881.39019
DOI: 10.1007/BF02755444
published in: Aequationes Mathematicae
publication date: 1998-01-13T00:00:00Z
full work available at URL: https://eudml.org/doc/137692
review text: The author offers a new proof and extension of a representation theorem by \textit{P. Šemrl} [Proc. Am. Math. Soc. 119, No. 4, 1105-1113 (1993; Zbl 0803.15024), cf. also ibid. 120, No. 2, 515-518 (1994; Zbl 0816.47040)] with aid of Jordan *-derivation pairs, which are defined as follows. Let \(K\) be a ring with involution *. The pair \(E, F\) of additive mappings of \(K\) into itself is a Jordan *-derivation pair if they satisfy the functional equation \(E(xyx)=E(x)y^*x^*+xF(y)x^*+xyE(x)\) for all \(x,y\in K\) and the similar equation with \(E\) and \(F\) interchanged.
reviewed by: János Aczél
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 16W10
Mathematics Subject Classification ID: 16D10
Mathematics Subject Classification ID: 46C15
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 16W25
zbMATH DE Number: 1053597
zbMATH Keywords: vector spaces
zbMATH Keywords: quadratic functionals
zbMATH Keywords: sesquilinear
zbMATH Keywords: quasi-quadratic functionals
zbMATH Keywords: quadratic functional equation
zbMATH Keywords: representation
zbMATH Keywords: Jordan *-derivations
zbMATH Keywords: \(C^*\)-algebras
zbMATH Keywords: pre-Hilbert
zbMATH Keywords: unital modules
zbMATH Keywords: derivation pairs
author: Borut Zalar
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1053597