On Derivations of Operator Algebras with Involution

Demonstratio mathematica

article

Nejc Širovnik¹  Joso Vukman² 

[1] FNM UNIVERSITY OF MARIBOR Koroška Cesta 160 2000 MARIBOR;INSTITUTE OF MATHEMATICS, PHYSICS AND MECHANICS DEPARTMENT IN MARIBOR

关键词: and phrases ring;    *-ring;    prime ring;    semiprime ring;    Banach space;    Hilbert space;    standard operator algebra;    derivation;    Jordan derivation.;   

DOI  :  10.2478/dema-2014-0063

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

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.

【 授权许可】

CC BY