Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Bounds for Nearly Best Approximations

Rudolf Wegmann
Proceedings of the American Mathematical Society
Vol. 52, No. 1 (Oct., 1975), pp. 252-256
DOI: 10.2307/2040140
Stable URL: http://www.jstor.org/stable/2040140
Page Count: 5
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Bounds for Nearly Best Approximations
Preview not available

Abstract

Let X be a uniformly convex space and ψ be the inverse function of the modulus of convexity δ(·). Assume here that ψ is a concave function. Let V be a linear subspace of X and let f in X be such that $\|f\| = 1 = \min\{\|f - \nu\|: \nu \epsilon V\}$. Then for $0 < \delta \leq 1$ and for ν in V with |f - ν| ≤ 1 + δ, it follows that |ν| ≤ K · ψ(δ). Let T be a compact Hausdorff-space and V a finite-dimensional subspace of C(T, X). When V has the interpolation property (Pm) with dim V = m · dim X, then the same type of estimate as above holds.

Page Thumbnails

  • Thumbnail: Page 
252
    252
  • Thumbnail: Page 
253
    253
  • Thumbnail: Page 
254
    254
  • Thumbnail: Page 
255
    255
  • Thumbnail: Page 
256
    256