On proximinality and sets of operators. I. Best approximation by finite rank operators

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Abstract

In this paper it is shown that Kn(X, C0, (Q)) is proximinal in L(X, C0(Q)) when X* is uniformly convex, thus solving Problem 5.2.3 of Deutsch, Mach and, Saatkamp (J. Approx. Theory 33 (1981), 199-213). The solutions of Problem 5.2.5 of Deutsch, et al. and the of problem 5.B of Franchetti and Cheney (Boll. Un Mat. Ital. B(5) 18 (1981), 1003-1015) are also included.

Original languageEnglish
Pages (from-to)132-145
Number of pages14
JournalJournal of Approximation Theory
Volume47
Issue number2
DOIs
Publication statusPublished - 1986

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ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Mathematics(all)
  • Applied Mathematics

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