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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

A characterization of best $ \Phi $-approximants


Authors: D. Landers and L. Rogge
Journal: Trans. Amer. Math. Soc. 267 (1981), 259-264
MSC: Primary 46E30; Secondary 41A50
MathSciNet review: 621986
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Abstract: Let $ T$ be an operator from an Orlicz space $ {L_\Phi }$ into itself. It is shown in this paper that four algebraic conditions and one integration condition assure that $ T$ is the best $ \Phi $-approximator, given a suitable $ \sigma $-lattice.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0621986-9
PII: S 0002-9947(1981)0621986-9
Keywords: Best approximants, $ \sigma $-lattices, conditional expectations, characterization
Article copyright: © Copyright 1981 American Mathematical Society