Izvorni znanstveni članak

https://doi.org/10.3336/gm.52.2.04

On certain equation related to derivations on standard operator algebras and semiprime rings

Irena Kosi-Ulbl orcid.org/0000-0002-9908-0877 ; Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia

Sažetak

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) → L (X) satisfying the relation D(Am+n)=D(Am)An+AmD(An) for all A A(X) and some fixed integers m≥1,n≥1. 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).

Ključne riječi

Prime ring; semiprime ring; Banach space; standard operator algebra; derivation; Jordan derivation

Hrčak ID:

189331

URI

https://hrcak.srce.hr/189331

Datum izdavanja:

13.11.2017.

Posjeta: 1.347 *