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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On approximation by rationals from a hyperplane
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by Gerhard Gierz and Boris Shekhtman PDF
Proc. Amer. Math. Soc. 96 (1986), 452-454 Request permission

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
  • Donald J. Newman, Approximation with rational functions, CBMS Regional Conference Series in Mathematics, vol. 41, Conference Board of the Mathematical Sciences, Washington, D.C., 1979. Expository lectures from the CBMS Regional Conference held at the University of Rhode Island, Providence, R.I., June 12–16, 1978. MR 539314
  • Helmut H. Schaefer, Banach lattices and positive operators, Die Grundlehren der mathematischen Wissenschaften, Band 215, Springer-Verlag, New York-Heidelberg, 1974. MR 0423039
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • 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