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

Ghawadrah, Ghadeer

doi:10.1090/proc12712

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