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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Non-isomorphic complemented subspaces of the reflexive Orlicz function spaces $L^{\Phi }[0,1]$
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by Ghadeer Ghawadrah PDF
Proc. Amer. Math. Soc. 144 (2016), 285-299 Request permission

Abstract:

In this note we show that the number of isomorphism classes of complemented subspaces of a reflexive Orlicz function space $L^{\Phi }[0,1]$ is uncountable, as soon as $L^{\Phi }[0,1]$ is not isomorphic to $L^{2}[0,1]$. Also, we prove that the set of all separable Banach spaces that are isomorphic to such an $L^{\Phi }[0,1]$ is analytic non-Borel. Moreover, by using the Boyd interpolation theorem we extend some results on $L^{p}[0,1]$ spaces to the rearrangement invariant function spaces under natural conditions on their Boyd indices.
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Additional Information
  • Ghadeer Ghawadrah
  • Affiliation: Université Paris VI, Institut de Mathématiques de Jussieu, Case 247, 4 place Jussieu, 75252 Paris Cedex 05, France
  • Email: ghadeer.ghawadrah@imj-prg.fr
  • Received by editor(s): August 9, 2014
  • Received by editor(s) in revised form: October 23, 2014, December 19, 2014, and December 20, 2014
  • Published electronically: May 28, 2015
  • Communicated by: Thomas Schlumprecht
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 285-299
  • MSC (2010): Primary 46B20; Secondary 54H05
  • DOI: https://doi.org/10.1090/proc12712
  • MathSciNet review: 3415596