On derivations of operator algebras with involutionŠirovnik, Nejc (Avtor) Vukman, Joso (Avtor) mathematicsprime ringssemiprime ringsderivationJordan derivationBanach spaceThe 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.De Gruyter20142017-03-31 09:51:33Znanstveno delo65330ISSN: 0420-1213UDK: 512.55OceCobissID: 14069256COBISS_ID: 20972040ISSN pri članku: 0420-1213NUK URN: URN:SI:UM:DK:YRJ3WIVIsl