Izvorni znanstveni članak

https://doi.org/10.3336/gm.50.2.07

ON CERTAIN IDENTITY RELATED TO JORDAN *-DERIVATIONS

Irena Kosi-Ulbl orcid.org/0000-0002-9908-0877 ; Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia
Joso Vukman ; Koroška cesta 57, 2000 Maribor, Slovenia

Sažetak

In this paper we prove the following result. Let H be a real or complex Hilbert space, let L(H) be the algebra of all bounded linear operators on H and let A(H) ⊆ L(H) be a standard operator algebra. Suppose we have an additive mapping D:A(H) → L(H) satisfying the relation D(An)=D(A)A* n-1+AD(An-2)A* +An-1D(A) for all A A(H) and some fixed integer n>1. In this case there exists a unique B L(H) such that D(A)=BA*-AB holds for all A A(H).

Ključne riječi

Ring; ring with involution; prime ring; semiprime ring; Hilbert space; standard operator algebra; *-derivation; Jordan *-derivation

Hrčak ID:

150137

URI

https://hrcak.srce.hr/150137

Datum izdavanja:

29.12.2015.

Posjeta: 1.284 *