On (m,n,l)-Jordan Centralizers of Some Algebras

2011/05/30 by Jianbin Guo, Guo, Jianbin, Jiankui Li +3
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.1105.5976

arxiv created 2011/06/15 · arxiv updated 2011/06/16

Abstract

Let A be a unital algebra over the complex field ℂ. A linear mapping δ from A into itself is called a weak (m,n,l)-Jordan centralizer if (m+n+l)δ(A²)-mδ(A)A-nAδ(A)-lAδ(I)A∈ ℂI for every A∈ A, where m≥0, n≥0, l≥0 are fixed integers with m+n+l≠ 0. In this paper, we study weak (m,n,l)-Jordan centralizer on generalized matrix algebras and some reflexive algebras algL, where L is CSL or satisfies \vee\L: L∈ J(L)\=X or \wedge\L_-: L∈ J(L)\=(0), and prove that each weak (m,n,l)-Jordan centralizer of these algebras is a centralizer when m+l≥1 and n+l≥1.

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