Lu Shijie.A Note on Generalized Derivation Ranges[J].Chinese Annals of Mathematics B,1985,6(3):261~268
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Authors：
Lu Shijie;
Abstract：
This paper is devoted to the generalized derivations determined by compact operators acting on Banach spaces. The author introduces the concept of “family of approximately linearly indepedent vectors” and employs this concept to prove the following result: Let X,Y be Banach spaces, A\in B(X),B\in B(Y) be compact operators. Then mathscr(T)_AB has closed range if and only if both A and B have closed range.
