On a functional equation related to two-sided centralizers



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:RR
3T(xn) = T(x)xn-1 + xT(xn-2)x + xn-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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Published : 2018-01-31


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

Irena Kosi-Ulbl  irena.kosi@um.si
Faculty of Mechanical Engineering, University of Maribor, Slovenia  Slovenia



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