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Title:General preservers of quasi-commutativity on self-adjoint operators
Authors:Kuzma, Bojan (Author)
Dolinar, Gregor (Author)
Files:URL http://dx.doi.org/10.1016/j.jmaa.2009.11.007
 
Language:English
Work type:Not categorized
Tipology:1.01 - Original Scientific Article
Organization:IAM - Andrej Marušič Institute
Abstract:Let ▫$H$▫ be a separable Hilbert space and▫ ${\mathcal B}_{sa}(H)▫$ the set of all bounded linear self-adjoint operators. We say that ▫$A, B \in {\mathcal B}_{sa}(H)$▫ quasi-commute if there exists a nonzero ▫$\xi \in \mathbb{C}$▫ suchthat ▫$AB=\xi BA$▫. Bijective maps on ▫${\mathcal B}_{sa}(H)$▫ which preserve quasi-commutativity in both directions are classified.
Keywords:mathematics, linear algebra, general preserver, self-adjoint operator, quasi-commutativity
Year of publishing:2010
Number of pages:str. 567-575
Numbering:Vol. 364, iss. 2
ISSN:0022-247X
UDC:512.643
COBISS_ID:15532889 Link is opened in a new window
Views:704
Downloads:42
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Secondary language

Language:Slovenian
Title:Splošni ohranjevalci kvazi-komutativnosti na sebi-adjungiranih operatorjih
Abstract:Naj bo ▫$H$▫ separabilen Hilbertov prostor in naj bo ▫${\mathcal B}_{sa}(H)$▫ množica vseh omejenih linearnih sebi-adjungiranih operatorjev. Pravimo, da operatorja ▫$A, B \in {\mathcal B}_{sa}(H)$▫ kvazi-komutirata, če obstaja tak neničelni skalar ▫$\xi \in \mathbb{C}$▫, da je ▫$AB=\xi BA$▫. V članku klasificiramo bijektivne preslikave na ▫${\mathcal B}_{sa}(H)$▫, ki ohranjajo kvazi-komutativnost v obeh smereh.
Keywords:matematika, linearna algebra, splošni ohranjevalci, sebi-adjungiran operator, kvazi-komutativnost

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