Approximation by certain subspaces in the banach space of continuous vector-valued functions

Dan Amir, Frakk Deutsch

Research output: Contribution to journalArticlepeer-review

Abstract

A theory of best approximation is developed in the normed linear space C(T, E), the space of E-valued bounded continuous functions on the locally compact Hausdorff space T, with the supremum norm. The approximating functions belong to the subspace CF(T, E) of C(T, E) consisting of those functions which have "limit at infinity" which lies in the subspace F of the normed linear space E. A distance formula is obtained, and a selection for the metric projection onto Cf(T, E) is constructed which has many desirable properties. The theory includes study of best approximation in l by the subspace c0, and closely parallels the known theory of best approximation by M-ideals (although our subspace is not an M-ideal, in general).

Original languageEnglish
Pages (from-to)254-270
Number of pages17
JournalJournal of Approximation Theory
Volume27
Issue number3
DOIs
StatePublished - Nov 1979

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