1Department of Mathematics, Aligarh Muslim University 2Department of Mathematics, Aligarh Muslim University, Aligarh-202002
Acta mathematica Universitatis Comenianae, Tome 85 (2016) no. 1, pp. 21-28
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Nadeem Ur Rehman; T. Bano; Nadeem Ur Rehman; T. Bano. A result on functional equations in semiprime rings and standard operator algebras. Acta mathematica Universitatis Comenianae, Tome 85 (2016) no. 1, pp. 21-28. http://geodesic.mathdoc.fr/item/AMUC_2016_85_1_a2/
@article{AMUC_2016_85_1_a2,
author = {Nadeem Ur Rehman and T. Bano and Nadeem Ur Rehman and T. Bano},
title = { A result on functional equations in semiprime rings and standard operator algebras},
journal = {Acta mathematica Universitatis Comenianae},
pages = {21--28},
year = {2016},
volume = {85},
number = {1},
url = {http://geodesic.mathdoc.fr/item/AMUC_2016_85_1_a2/}
}
TY - JOUR
AU - Nadeem Ur Rehman
AU - T. Bano
AU - Nadeem Ur Rehman
AU - T. Bano
TI - A result on functional equations in semiprime rings and standard operator algebras
JO - Acta mathematica Universitatis Comenianae
PY - 2016
SP - 21
EP - 28
VL - 85
IS - 1
UR - http://geodesic.mathdoc.fr/item/AMUC_2016_85_1_a2/
ID - AMUC_2016_85_1_a2
ER -
%0 Journal Article
%A Nadeem Ur Rehman
%A T. Bano
%A Nadeem Ur Rehman
%A T. Bano
%T A result on functional equations in semiprime rings and standard operator algebras
%J Acta mathematica Universitatis Comenianae
%D 2016
%P 21-28
%V 85
%N 1
%U http://geodesic.mathdoc.fr/item/AMUC_2016_85_1_a2/
%F AMUC_2016_85_1_a2
Let $X$ be a real or complex Banach space, let $L(X)$ be the algebra of all bounded linear operators of $X$ into itself andlet $A(X)\subset L(X)$ be a standard operator algebra. Suppose there exist linear mappings $D,G : A(X) \to L(X)$ satisfying the relations $2D(A^n) = D(A^{n-1})A+A^{n-1}G(A)+ G(A)A^{n-1}+AG(A^{n-1})$ and 2G(A^n) = G(A^{n-1})A+A^{n-1}D(A)+ D(A)A^{n-1}+AD(A^{n-1})$ for all $A\in A(X)$. Then there exists some fixed $B \in L(X)$ such that $D(A) = G(A) = [A;B]$ holds for all $A \in A(X)$.
