Constrained Approximation in Banach Spaces |
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Authors: | Smith |
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Institution: | (1) School of Mathematics University of Leeds Leeds LS2 9JT United Kingdom mpsmith@amsta.leeds.ac.uk, UK |
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Abstract: |
Abstract. We consider the problem of approximating vectors from a complemented subspace Z
+
of a Banach space X by the projections onto Z
+
of vectors from a subspace Y
+
with a norm constraint on their projections onto the complementary subspace. Sufficient conditions are found for the existence
of a unique best approximant and a characterization via a critical point equation is provided, thus extending known results
on Hilbert spaces. These results are then applied in the case that X is L
p
(T), where T denotes the unit circle, Z
+
consists of functions supported on a subset of the circle, and Y
+
is the corresponding Hardy space. |
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Keywords: | , Extremal problems, Analytic approximation, Hardy spaces, AMS Classification, 41A29, 46E15, |
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