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

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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.## References

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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