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A Characterization of Best Simultaneous Approximations

✍ Scribed by G.A. Watson

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
165 KB
Volume
75
Category
Article
ISSN
0021-9045

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✦ Synopsis

The problem of approximating a finite number of functions simultaneously is considered. For a general class of norms, a characterization of best approximations is given. The result generalizes recent work concerned specifically with the Chebyshev norm. 1993 Academic Press, Inc.

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## Abstract Let __Y__ be a reflexive subspace of the Banach space __X__, let (Ξ©, Ξ£, __ΞΌ__) be a finite measure space, and let __L__~∞~(__ΞΌ, X__) be the Banach space of all essentially bounded __ΞΌ__ ‐Bochner integrable functions on Ξ© with values in __X__, endowed with its usual norm. Let us suppose