Phelps type duality results in best approximation

Ştefan Cobzaş

doi:10.33993/jnaat311-706

Authors

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

DOI:

https://doi.org/10.33993/jnaat311-706

Keywords:

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

Abstract views: 285

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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References

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