J. Alaminos (Author), Matej Brešar (Author), J. Extremera (Author), A. R. Villena (Author)

Abstract

Naj bosta ▫$A$▫ in ▫$B$▫ ▫$C^\ast$▫-algebri, ▫$X$▫ naj bo bistveni Banachov ▫$A$▫-bimodul in naj bosta ▫$T \colon A \to B$▫ in ▫$S \colon A \to X$▫ zvezni linearni preslikavi; ▫$T$▫ naj bo surjektivna. Denimo, da je ▫$T(a)T(b) + T(b)T(a) = 0$▫ in ▫$S(a)b + bS(a) + aS(b) + S(b)a = 0$▫, kadarkoli ▫$a, b \in A$▫ zadoščata ▫$ab = ba = 0$▫. Dokažemo, da je ▫$T = w\Phi$▫ in ▫$S = D + w\Psi$▫, kjer ▫$w$▫ leži v centru multiplikatorske algebre ▫$B$▫, ▫$\Phi\colon A \to B$▫ je jordanski epimorfizem, ▫$D \colon A \to X$▫ je odvajanje in ▫$\Psi \colon A \to X$▫ je bimodulski homomorfizem.

Keywords

matematika;teorija operatorjev;▫$C^\ast$▫-algebra;homomorfizem;jordanski homomorfizem;odvajanje;jordansko odvajanje;ohranjevalec ničelnega produkta;mathematics;operator theory;homomorphism;Jordan homomorphism;derivation;Jordan derivation;zero-product-preserving map;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
UDC: 517.98
COBISS: 15703129 Link will open in a new window
ISSN: 0013-0915
Views: 57
Downloads: 320
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Other data

Secondary language: Slovenian
Secondary title: Karakterizacija jordanskih preslikav na C[zvezdica]-algebrah z ničelnim produktom
Secondary abstract: Let ▫$A$▫ and ▫$B$▫ be ▫$C^\ast$▫-algebras, let ▫$X$▫ be an essential Banach ▫$A$▫-bimodule and let ▫$T \colon A \to B$▫ and ▫$S \colon A \to X$▫ be continuous linear maps with ▫$T$▫ surjective. Suppose that ▫$T(a)T(b) + T(b)T(a) = 0$▫ and ▫$S(a)b + bS(a) + aS(b) + S(b)a = 0$▫ whenever ▫$a, b \in A$▫ are such that ▫$ab =ba = 0$▫. We prove that then ▫$T = w\Phi$▫ and ▫$S = D + w\Psi$▫, where ▫$w$▫ lies in the centre of the multiplier algebra of ▫$B$▫, ▫$\Phi\colon A \to B$▫ is a Jordan epimorphism, ▫$D \colon A \to X$▫ is a derivation and ▫$\Psi \colon A \to X$▫ is a bimodule homomorphism.
Secondary keywords: matematika;teorija operatorjev;▫$C^\ast$▫-algebra;homomorfizem;jordanski homomorfizem;odvajanje;jordansko odvajanje;ohranjevalec ničelnega produkta;
URN: URN:SI:UM:
Type (COBISS): Not categorized
Pages: str. 543-555
Volume: Vol. 53
Issue: iss. 3
Chronology: 2010
ID: 1475239