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Demonstratio Mathematica

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Volume 47, Issue 4


On Derivations of Operator Algebras with Involution

Nejc Širovnik
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/ Joso Vukman
Published Online: 2014-12-11 | DOI: https://doi.org/10.2478/dema-2014-0063


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


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About the article

Received: 2013-03-01

Published Online: 2014-12-11

Published in Print: 2014-12-01

Citation Information: Demonstratio Mathematica, Volume 47, Issue 4, Pages 784–790, ISSN (Online) 2391-4661, ISSN (Print) 0420-1213, DOI: https://doi.org/10.2478/dema-2014-0063.

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© by Nejc Širovnik. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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