Glasnik matematički, Vol. 50 No. 2, 2015.
Original scientific paper
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
Abstract
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).
Keywords
Ring; ring with involution; prime ring; semiprime ring; Hilbert space; standard operator algebra; *-derivation; Jordan *-derivation
Hrčak ID:
150137
URI
Publication date:
29.12.2015.
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