On derivations of operator algebras with involution

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;ne zaključna dela;mathematics;prime rings;semiprime rings;derivation;Jordan derivation;Banach space;

Data

Language:	English
Year of publishing:	2014
Typology:	1.01 - Original Scientific Article
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	De Gruyter
UDC:	512.55
COBISS:	20972040
ISSN:	0420-1213
Views:	1197
Downloads:	355
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary keywords:	Algebra;
URN:	URN:SI:UM:
Type (COBISS):	Scientific work
Pages:	str. 784-790
Volume:	ǂVol. ǂ47
Issue:	ǂno. ǂ4
Chronology:	2014
ID:	9595928