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On approximation by rationals from a hyperplane


Authors: Gerhard Gierz and Boris Shekhtman
Journal: Proc. Amer. Math. Soc. 96 (1986), 452-454
MSC: Primary 41A20
DOI: https://doi.org/10.1090/S0002-9939-1986-0822438-3
MathSciNet review: 822438
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Abstract: Let $ E \subset C(K)$ be a subspace of continuous functions defined on a compact Hausdorff space $ K$. We characterize those subspaces of codimension 1 for which the rational functions with denominators and enumerators from $ E$ are dense. The condition for the density of this very nonlinear set of functions turns out to be a linear separation condition.


References [Enhancements On Off] (What's this?)

  • [1] D. J. Newman, Approximation with rational functions, CBMS Regional Conf. Ser. in Math., no. 41, Amer. Math. Soc., Providence, R. I., 1979. MR 539314 (84k:41019)
  • [2] H. H. Schaefer, Banach lattices and positive operators, Springer-Verlag, Berlin and New York, 1974. MR 0423039 (54:11023)

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DOI: https://doi.org/10.1090/S0002-9939-1986-0822438-3
Article copyright: © Copyright 1986 American Mathematical Society

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