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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Flat Orlicz spaces
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by A. J. Pach, M. A. Smith and B. Turett PDF
Proc. Amer. Math. Soc. 81 (1981), 528-530 Request permission

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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Additional Information
  • © Copyright 1981 American Mathematical Society
  • 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