%0 Journal Article
%T On certain equation related to derivations on standard operator algebras and semiprime rings
%A Kosi-Ulbl
%A Irena
%J -
%D 2017
%R 10.3336/gm.52.2.04
%X Sa£¿etak In this paper we prove the following result, which is related to a classical result of Chernoff. Let X be a real or complex Banach space, let A(X) be a standard operator algebra on X and let L (X) be an algebra of all bounded linear operators on X. Suppose we have a linear mapping D: A(X) ¡ú L (X) satisfying the relation D(Am+n)=D(Am)An+AmD(An) for all A A(X) and some fixed integers m¡Ý1,n¡Ý1. In this case there exists B L (X), such that D(A)=AB-BA holds for all A F(X), where F (X) denotes the ideal of all finite rank operators in L (X). Besides, D(Am)=AmB-BAm is fulfilled for all A A(X)
%K Prime ring
%K semiprime ring
%K Banach space
%K standard operator algebra
%K derivation
%K Jordan derivation
%U https://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=278922