Journal Article

SMOOTH NORMS AND APPROXIMATION IN BANACH SPACES OF THE TYPE π’ž(K)

Petr HΓ‘jek and Richard Haydon

inΒ The Quarterly Journal of Mathematics

Volume 58, issue 2, pages 221-228
Published in print June 2007 | ISSN: 0033-5606
Published online March 2007 | e-ISSN: 1464-3847 | DOI:Β https://dx.doi.org/10.1093/qmath/ham010
SMOOTH NORMS AND APPROXIMATION IN BANACH SPACES OF THE TYPE π’ž(K)

Show Summary Details

Preview

Abstract

Two results are proved about the Banach space X = π’ž(K), where K is compact and Hausdorff. The first concerns smooth approximation: let m be a positive integer or ∞; we show that if there exists on X a non-zero function of class π’žm with bounded support, then all continuous real-valued functions on X can be uniformly approximated by functions of class π’žm. The second result is that if X admits a norm, equivalent to the supremum norm, with locally uniformly convex dual norm, then X also admits an equivalent norm that is of class π’žβˆž (except at 0).

Journal Article.Β  0 words.Β 

Subjects: Pure Mathematics

Full text: subscription required

How to subscribe Recommend to my Librarian

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content. subscribe or login to access all content.