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Title:Characterizing Jordan maps on C [ast]-algebras through zero products
Authors:ID Alaminos, J. (Author)
ID Brešar, Matej (Author)
ID Extremera, J. (Author)
ID Villena, A. R. (Author)
Files:URL http://dx.doi.org/10.1017/S0013091509000534
 
Language:English
Work type:Not categorized
Typology:1.01 - Original Scientific Article
Organization:FNM - Faculty of Natural Sciences and Mathematics
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 ▫$T = wPhi$▫ in ▫$S = D + wPsi$▫, kjer ▫$w$▫ leži v centru multiplikatorske algebre ▫$B$▫, ▫$Phicolon A to B$▫ 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, ▫$C^ast$▫-algebra, homomorphism, Jordan homomorphism, derivation, Jordan derivation, zero-product-preserving map
Year of publishing:2010
Number of pages:str. 543-555
Numbering:Vol. 53, iss. 3
PID:20.500.12556/DKUM-51871 New window
UDC:517.98
ISSN on article:0013-0915
COBISS.SI-ID:15703129 New window
NUK URN:URN:SI:UM:DK:8PIBOJEQ
Publication date in DKUM:10.07.2015
Views:1114
Downloads:47
Metadata:XML DC-XML DC-RDF
Categories:Misc.
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Record is a part of a journal

Title:Proceedings of the Edinburgh Mathematical Society
Shortened title:Proc. Edinb. Math. Soc.
Publisher:Scottish Academic Press
ISSN:0013-0915
COBISS.SI-ID:27124480 New window

Secondary language

Language:Unknown
Title:Karakterizacija jordanskih preslikav na C[zvezdica]-algebrah z ničelnim produktom
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 ▫$T = wPhi$▫ and ▫$S = D + wPsi$▫, where ▫$w$▫ lies in the centre of the multiplier algebra of ▫$B$▫, ▫$Phicolon A to B$▫ is a Jordan epimorphism, ▫$D colon A to X$▫ is a derivation and ▫$Psi colon A to X$▫ is a bimodule homomorphism.


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