On a functional equation related to two-sided centralizers

Irena Kosi-Ulbl

Published: 2018-01-31

Vol. 32 (2018)

On a functional equation related to two-sided centralizers

Irena Kosi-Ulbl

Abstract

The main aim of this manuscript is to prove the following result. Let n>2 be a fixed integer and R be a k-torsion free semiprime ring with identity, where k∈{2, n−1, n}. Let us assume that for the additive mapping T:R→R
3T(xⁿ) = T(x)x^n-1 + xT(x^n-2)x + x^n-1T(x), x∈R,
is also fulfilled. Then T is a two-sided centralizer.

Keywords:

prime ring , semiprime ring , Banach space , standard operator algebra , left (right) centralizer , left (right) Jordan centralizer , two-sided centralizer

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Kosi-Ulbl, I. (2018). On a functional equation related to two-sided centralizers. Annales Mathematicae Silesianae, 32, 227–235. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13922

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Vol. 32 (2018)
Published: 2018-08-24

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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