Glasnik matematički, Vol. 47 No. 1, 2012.
Original scientific paper
https://doi.org/10.3336/gm.47.1.09
On certain functional equation arising from (m,n)- Jordan centralizers in prime rings
Nina Peršin
; Prušnikova 48, 2000 Maribor, Slovenia
Joso Vukman
; Department of Mathematics and Computer Science, Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
Abstract
The purpose of this paper is to prove the following result. Let m≥ 1,n≥ 1 be some fixed integers and let R be a prime ring with char(R)=0 or (m+n)2 < char (R). Suppose there exists an additive mapping T:R → R satisfying the relation 2(m+n)2T(x3)=m(2m+n)T(x)x2+2mnxT(x)x+n(2n+m)x2T(x) for all x R. In this case T is a two-sided centralizer.
Keywords
Ring; prime ring; semiprime ring; Banach space; Hilbert space; algebra of all bounded linear operators; standard operator algebra; derivation; Jordan derivation; left (right) centralizer; two-sided centralizer; left (right) Jordan centralizer; (m,n)-Jordan centralizer
Hrčak ID:
82575
URI
Publication date:
3.6.2012.
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