ON CERTAIN FUNCTIONAL EQUATION IN SEMIPRIME RINGS AND STANDARD OPERATOR ALGEBRAS

The main purpose of this paper is to prove the following result, which is related to a classical result of Chernoff. Let X be a real or complex Banach space, let L (X) be the algebra of all bounded linear operators on X and let A(X) C L (X) be a standard operator algebra. Suppose there exists a line...

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Bibliographic Details
Published inCubo (Temuco, Chile) Vol. 16; no. 1; pp. 73 - 80
Main Author Širovnik, Nejc
Format Journal Article
LanguagePortuguese
Published Universidad de La Frontera. Departamento de Matemática y Estadística 2014
Subjects
MATHEMATICS
MATHEMATICS, APPLIED
Prime ring
39B42
46B99
derivation
semiprime ring
Banach space
standard operator algebra
Jordan derivation
16N60
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Summary:The main purpose of this paper is to prove the following result, which is related to a classical result of Chernoff. Let X be a real or complex Banach space, let L (X) be the algebra of all bounded linear operators on X and let A(X) C L (X) be a standard operator algebra. Suppose there exists a linear mapping D : A (X) ͢ L (X) satisfying the relation 2D (An) = D (An-1) A+An-1 D (A) + D (A) An-1+ AD (An-1) for all A e A (X), where n > 2 is some fixed integer. In this case D is of the form D (A) = [A, B] for all A e A (X) and some fixed B e L (X), which means that D is a linear derivation. In particular, D is continuous.
ISSN:0719-0646
0719-0646
DOI:10.4067/S0719-06462014000100007