General preservers of quasi-commutativity on self-adjoint operators
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.
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.
2010
2016-04-08 16:46:51
1033
mathematics, linear algebra, general preserver, self-adjoint operator, quasi-commutativity
matematika, linearna algebra, splošni ohranjevalci, sebi-adjungiran operator, kvazi-komutativnost
r6
Gregor
Dolinar
70
Bojan
Kuzma
70
ISSN
2
0022-247X
UDK
4
512.643
OceCobissID
13
3081231
COBISS.SI-ID
3
15532889
0
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2016-04-08 16:46:51