Nejc Širovnik (Author), Joso Vukman (Author)

Abstract

The purpose of this paper is to prove the following result. Let X be a complex Hilbert space, let L(X) be an algebra of all bounded linear operators on X and let A(X) ⊂ L(X) be a standard operator algebra, which is closed under the adjoint operation. Suppose there exists a linear mapping D : A(X) → L(X) satisfying the relation 2D(AA*A) = D(AA*)A + AA*D(A) + D(A)A*A + AD(A*A) for all A ∈ A(X). In this case, D is of the form D(A) = [A,B] for all A ∈ A(X) and some fixed B ∈ L(X), which means that D is a derivation.

Keywords

matematika;algebra;prakolobarji;polprakolobarji;odvajanje;jordansko odvajanje;Banachovi prostori;mathematics;prime rings;semiprime rings;derivation;Jordan derivation;Banach space;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
UDC: 512.55
COBISS: 20972040 Link will open in a new window
ISSN: 0420-1213
Views: 678
Downloads: 310
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Other data

Secondary language: Slovenian
Secondary keywords: matematika;algebra;prakolobarji;polprakolobarji;odvajanje;jordansko odvajanje;Banachovi prostori;
URN: URN:SI:UM:
Type (COBISS): Scientific work
Pages: str. 784-790
Volume: ǂVol. ǂ47
Issue: ǂno. ǂ4
Chronology: 2014
ID: 9595928