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Existence and characterization of best φ-approximations by linear subspaces

Authors
  • Benavente, Ana
  • Favier, Sergio
  • Levis, Fabián
Type
Published Article
Journal
Advances in Pure and Applied Mathematics
Publisher
De Gruyter
Publication Date
Mar 16, 2017
Volume
8
Issue
3
Pages
209–217
Identifiers
DOI: 10.1515/apam-2015-0069
Source
De Gruyter
Keywords
License
Yellow

Abstract

Given an Orlicz space L φ {L^{\varphi}} , we give very relaxed sufficient conditions on φ to ensure that there exists a best φ-approximation from any finite dimensional bounded linear subspace S ⊂ L φ {S\subset L^{\varphi}} . In addition, given an operator T, defined from L φ {L^{\varphi}} into itself, we give necessary and sufficient conditions on T to ensure that this is a best φ-approximation operator from a linear subspace S.

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