Taiwanese Journal of Mathematics

ON CENTRALIZERS OF SEMISIMPLE $H^{\ast}−$ALGEBRAS

Joso Vukman and Irena Kosi-Ulbl

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Abstract

In this paper we prove the following result. Let $A$ be a semisimple $H^{\ast}-$algebra and let $T: A \rightarrow A$ be an additive mapping satisfying the relation $2T(x^{m+n+1}) = x^{m} T(x) x^{n} + x^{n} T(x) x^{m}$, for all $x \in A$ and some nonnegative integers $m,n$ such that $ m+n \neq 0$. In this case $T$ is a left and a right centralizer.

Article information

Source
Taiwanese J. Math., Volume 11, Number 4 (2007), 1063-1074.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500404803

Digital Object Identifier
doi:10.11650/twjm/1500404803

Mathematical Reviews number (MathSciNet)
MR2348552

Zentralblatt MATH identifier
1181.46039

Subjects
Primary: 16W10: Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx] 46K15: Hilbert algebras 39B05: General

Keywords
prime ring semiprime ring Banach space standard operator algebra $H^{\ast}-$algebra left (right) centralizer left (right) Jordan centraliz

Citation

Vukman, Joso; Kosi-Ulbl, Irena. ON CENTRALIZERS OF SEMISIMPLE $H^{\ast}−$ALGEBRAS. Taiwanese J. Math. 11 (2007), no. 4, 1063--1074. doi:10.11650/twjm/1500404803. https://projecteuclid.org/euclid.twjm/1500404803


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