Ajda Fošner (Author), Joso Vukman (Author)

Abstract

Naj bo ▫$H$▫ kompleksni Hilbertov prostor, ▫$\mathcal{B}(H)$▫ algebra vseh omejenih linearnih operatorjev na ▫$H$▫ ter ▫$\mathcal{A}(H)$▫ standardna operatorska algebra, zaprta za adjungiranje. Če je ▫$T: \mathcal{A}(H) \to \mathcal{B}(H)$▫ linearna preslikava, ki zadošča identiteti ▫$T(AA^\ast A) = T(A)A^\ast A - AT(A^\ast)A + AA^\ast T(A)$▫ za vsak ▫$A$▫ iz ▫$\mathcal{A}(H)$▫, potem je ▫$T(A) = AB + BA$▫ za vsak ▫$A$▫ iz A(H), kjer je ▫$B$▫ operator iz ▫$\mathcal{B}(H)$▫.

Keywords

matematika;algebra;kolobar;prakolobar;polprakolobar;Banachov prostor;Hilbertov prostor;standardna operatorska algebra;odvajanje;jordansko odvajanje;bicirkularni projektor;mathematics;ring;▫$^\ast$▫-ring;prime ring;semiprime ring;Banach space;Hilbert space;standard operator algebra;derivation;Jordan derivation;bicircular projection;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
UDC: 512.552
COBISS: 14661721 Link will open in a new window
ISSN: 0236-5294
Views: 42
Downloads: 3
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Other data

Secondary language: Slovenian
Secondary title: Nekatere funkcijske identitete na standardnih operatorskih algebrah
Secondary abstract: The main purpose of this paper is to prove the following result. Let ▫$H$▫ be a complex Hilbert space, let ▫$\mathcal{B}(H)$▫ be the algebra of all bounded linear operators on ▫$H$▫, and let ▫$\mathcal{A}(H) \subset{B}(H)$▫ be a standard operator algebra which is closed under the adjoint operation. Suppose that ▫$T: \mathcal{A}(H) \to \mathcal{B}(H)$▫ is a linear mapping satisfying ▫$T(AA^\ast A) = T(A)A^\ast A - AT(A^\ast)A + AA^\ast T(A)$▫ for all ▫$A \in \mathcal{A}(H)$▫. Then ▫$T$▫ is of the form ▫$T(A) = AB + BA$▫ for all ▫$A \in \mathcal{A}(H)$▫, where ▫$B$▫ is a fixed operator from ▫$\mathcal{B}(H)▫$. A result concerning functional equations related to bicircular projections is proved.
Secondary keywords: matematika;algebra;kolobar;prakolobar;polprakolobar;Banachov prostor;Hilbertov prostor;standardna operatorska algebra;odvajanje;jordansko odvajanje;bicirkularni projektor;
URN: URN:SI:UM:
Type (COBISS): Not categorized
Pages: str. 299-306
Volume: ǂVol. ǂ118
Issue: ǂno. ǂ4
Chronology: 2008
ID: 1473554