Wang, Yuwen; Pan, Shaorong An approximation problem of the finite rank operator in Banach spaces. (English) Zbl 1218.47028 Sci. China, Ser. A 46, No. 2, 245-250 (2003). 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)]. Cited in 7 Documents MSC: 47A58 Linear operator approximation theory 47B07 Linear operators defined by compactness properties 46B99 Normed linear spaces and Banach spaces; Banach lattices Keywords:Banach space; compact linear operator; bounded homogeneous operator; finite rank operator; approximation Citations:Zbl 0267.46012 PDFBibTeX XMLCite \textit{Y. Wang} and \textit{S. Pan}, Sci. China, Ser. A 46, No. 2, 245--250 (2003; Zbl 1218.47028)