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 -