On Two-Sided Centralizers of Rings and Algebras

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Abstract

In this paper we prove the following result. Let A be a semisimple H*−algebra and let T : A → A be an additive mapping satisfying the relation (n + 1)T(xnm+1) = T(x)xnm + xmT(x)x(n−1)m + · · · + xnmT(x), for all x ∈ A and some fixed integers m ≥ 1, n ≥ 1. In this case T is a two-sided centralizer.

Keywords

Prime ring , semiprime ring , Banach space , standard operator algebra , 𝐻*-algebra , left (right) centralizer , left (right) Jordan centralizer , two-sided centralizer
  • Joso Vukman Department of Mathematics and Computer Sciences, Faculty of Natural Sciences and Mathematics, University of Maribor, Koroska 160, 2000 Maribor, Slovenia.
  • Irena Kosi-Ulbl Faculty of Education, University of Maribor, Koroska 160, 2000 Maribor, Slovenia.
  • Pages: 211–222
  • Date Published: 2008-10-01
  • Vol. 10 No. 3 (2008): CUBO, A Mathematical Journal

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Published

2008-10-01

How to Cite

[1]
J. Vukman and I. Kosi-Ulbl, “On Two-Sided Centralizers of Rings and Algebras”, CUBO, vol. 10, no. 3, pp. 211–222, Oct. 2008.

Issue

Vol. 10 No. 3 (2008): CUBO, A Mathematical Journal

Section

Articles