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An approximation problem of the finite rank operator in Banach spaces. (English) Zbl 1218.47028

Summary: By the method of the geometry of Banach spaces, we prove that a bounded linear operator in Banach space is a compact linear one iff it can be uniformly approximated by a sequence of the finite rank bounded homogeneous operators, which reveals the essence of the counterexample given by P. Enflo [Acta Math. 130, 309–317 (1973; Zbl 0267.46012)].

MSC:

47A58 Linear operator approximation theory
47B07 Linear operators defined by compactness properties
46B99 Normed linear spaces and Banach spaces; Banach lattices

Citations:

Zbl 0267.46012
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