Abstract
In this paper identities related to derivations and centralizers on operator algebras are considered. We prove the following result which is related to a classical result of Chernoff. Let $X$ be a real or complex Banach space, let $L(X)$ and $F(X)$ be the algebra of all bounded linear operators and the ideal of all finite rank operators on $X$, respectively. Suppose there exist linear mappings $D,G : F(X) \to L(X)$ such that $D(A^2) = D(A)A + AG(A)$ and $G(A^2) = G(A)A + AD(A)$ is fulfilled for all $A \in F(X)$. In this case there exists $B \in L(X)$ such that $D(A) = G(A) = [A,B]$ holds for all $A \in F(X)$.
Citation
Joso Vukman. "IDENTITIES RELATED TO DERIVATIONS AND CENTRALIZERS ON STANDARD OPERATOR ALGEBRAS." Taiwanese J. Math. 11 (1) 255 - 265, 2007. https://doi.org/10.11650/twjm/1500404650
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