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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Flat Orlicz spaces


Authors: A. J. Pach, M. A. Smith and B. Turett
Journal: Proc. Amer. Math. Soc. 81 (1981), 528-530
MSC: Primary 46E30; Secondary 46B25
DOI: https://doi.org/10.1090/S0002-9939-1981-0601722-8
MathSciNet review: 601722
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Abstract: Let $ (\Omega ,\Sigma ,\mu )$ be a finite measure space that is not purely atomic and let $ \Phi $ be a Young function. It is shown that the Orlicz space $ {L^\Phi }(\mu )$ is flat if and only if either $ {L^\Phi }(\mu )$ contains an isometric copy of $ {l^\infty }{\text{or}}{L^\Phi }(\mu )$ is isometric to $ {L^1}(\mu )$.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0601722-8
Keywords: Orlicz space, flat Banach space
Article copyright: © Copyright 1981 American Mathematical Society

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