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http://dx.doi.org/10.14317/jami.2022.1129

AN IDENTITY ON STANDARD OPERATOR ALGEBRA  

SHUJAT, FAIZA (Department of Mathematics, Faculty of Science, Taibah University)
Publication Information
Journal of applied mathematics & informatics / v.40, no.5_6, 2022 , pp. 1129-1135 More about this Journal
Abstract
The purpose of this research is to find an extension of the renowned Chernoff theorem on standard operator algebra. Infact, we prove the following result: Let H be a real (or complex) Banach space and 𝓛(H) be the algebra of bounded linear operators on H. Let 𝓐(H) ⊂ 𝓛(H) be a standard operator algebra. Suppose that D : 𝓐(H) → 𝓛(H) is a linear mapping satisfying the relation D(AnBn) = D(An)Bn + AnD(Bn) for all A, B ∈ 𝓐(H). Then D is a linear derivation on 𝓐(H). In particular, D is continuous. We also present the limitations on such identity by an example.
Keywords
Semiprime ring; Banach space; standard operator algebra; derivation;
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Times Cited By KSCI : 1  (Citation Analysis)
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