Phelps type duality results in best approximation

Authors

  • Ştefan Cobzaş "Babeş Bolyai" University, Cluj-Napoca, Romania

Keywords:

best approximation, Hahn-Banach extension, \(M\)-ideals

Abstract

The aim of the present paper is to show that many Phelps type duality result, relating the extension properties of various classes of functions (continuous, linear continuous, bounded bilinear, Hölder-Lipschitz) with the approximation properties of some annihilating spaces, can be derived in a unitary and simple way from a formula for the distance to the kernel of a linear operator, extending the well-known distance formula to hyperplanes in normed spaces. The case of spaces \(c_0\) and \(l^\infty\) is treated in details.

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Published

2002-02-01

How to Cite

Cobzaş, Ştefan. (2002). Phelps type duality results in best approximation. Rev. Anal. Numér. ThéOr. Approx., 31(1), 29-43. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2002-vol31-no1-art5

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