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RUP
FAMNIT - Faculty of Mathematics, Science and Information Technologies
FHŠ - Faculty of Humanities
FM - Faculty of Management
FTŠ Turistica - Turistica – College of Tourism Portorož
FVZ - Faculty of Health Sciences
IAM - Andrej Marušič Institute
PEF - Faculty of Education
UPR - University of Primorska
ZUP - University of Primorska Press
COBISS
University of Primorska, University Library - all departments
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Title:
General preservers of quasi-commutativity on self-adjoint operators
Authors:
ID
Dolinar, Gregor
(Author)
ID
Kuzma, Bojan
(Author)
Files:
http://dx.doi.org/10.1016/j.jmaa.2009.11.007
Language:
English
Work type:
Not categorized
Typology:
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
PID:
20.500.12556/RUP-7731
ISSN:
0022-247X
UDC:
512.643
COBISS.SI-ID:
15532889
Publication date in RUP:
03.04.2017
Views:
2167
Downloads:
76
Metadata:
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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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