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:R→R
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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Faculty of Mechanical Engineering, University of Maribor, Slovenia Slovenia
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