On derivations of operator algebras with involution

• Autorzy: Širovnik N. , Vukman J.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

ring; *-ring; prime ring; semiprime ring; Banach space; Hilbert space; standard operator algebra; derivation; Jordan derivation

PL

pierścień; pierścień pierwszy; półpierścień pierwszy; przestrzeń Banacha; przestrzeń Hilberta; pochodne; pochodne Jordana

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 4
• Strony: 784--790
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Širovnik N.

• Department of Mathematics and Computer Science, FNM University of Maribor Koroška Cesta 160 2000 Maribor, Slovenia

autor

Vukman J.

• Institute of Mathematics, Physics and Mechanics Department in Maribor Gosposvetska 84 2000 Maribor, Slovenia

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