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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Bounds for nearly best approximations
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by Rudolf Wegmann PDF
Proc. Amer. Math. Soc. 52 (1975), 252-256 Request permission

Abstract:

Let $X$ be a uniformly convex space and $\psi$ be the inverse function of the modulus of convexity $\delta ( \cdot )$. Assume here that $\psi$ is a concave function. Let $V$ be a linear subspace of $X$ and let $f$ in $X$ be such that $||f|| = 1 = \min \{ ||f - v||:v\epsilon V\}$. Then for $0 < \delta \leqslant 1$ and for $v$ in $V$ with $||f - v|| \leqslant 1 + \delta$, it follows that $||v|| \leqslant K \cdot \psi (\delta )$. Let $T$ be a compact Hausdorff-space and $V$ a finite-dimensional subspace of $C(T,X)$. When $V$ has the interpolation property $({P_m})$ with $V = m \cdot \dim X$, then the same type of estimate as above holds.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 252-256
  • MSC: Primary 41A65
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0442563-1
  • MathSciNet review: 0442563