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Non-isomorphic complemented subspaces of the reflexive Orlicz function spaces $L^{\Phi }[0,1]$

Author: Ghadeer Ghawadrah
Journal: Proc. Amer. Math. Soc. 144 (2016), 285-299
MSC (2010): Primary 46B20; Secondary 54H05
Published electronically: May 28, 2015
MathSciNet review: 3415596
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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

Keywords: Orlicz function space, complemented subspaces, Cantor group, rearrangement invariant function space, well-founded tree, analytic, non-Borel
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
Article copyright: © Copyright 2015 American Mathematical Society