TY - JOUR

T1 - Approximation by certain subspaces in the banach space of continuous vector-valued functions

AU - Amir, Dan

AU - Deutsch, Frakk

PY - 1979/11

Y1 - 1979/11

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=27844536761&partnerID=8YFLogxK

U2 - 10.1016/0021-9045(79)90108-4

DO - 10.1016/0021-9045(79)90108-4

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AN - SCOPUS:27844536761

SN - 0021-9045

VL - 27

SP - 254

EP - 270

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

IS - 3

ER -