Phelps type duality results in best approximation
Keywords:best approximation, Hahn-Banach extension, \(M\)-ideals
AbstractThe 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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