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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Strong unicity of best approximations in $ L\sb \infty(S,\Sigma,\mu)$


Author: Ryszard Smarzewski
Journal: Proc. Amer. Math. Soc. 103 (1988), 113-116
MSC: Primary 41A50; Secondary 41A52, 46E10
MathSciNet review: 938653
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Abstract: We prove that the set of functions in a Banach space $ {L_\infty }(S,\sum ,\mu )$, which have a strongly unique best approximation in a finite dimensional subspace, is dense in the set of functions having a unique best approximation in the subspace.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0938653-6
PII: S 0002-9939(1988)0938653-6
Article copyright: © Copyright 1988 American Mathematical Society