Abstract
We show that ifl p(X),p ≠ 2, is finitely crudely representable in an Orlicz spaceL ϕ (which does not containc 0) then the Banach spaceX is isomorphic to a subspace ofL p. The same remains true forp = 2 whenL ϕ is 2-concave or 2-convex, or ifX has local unconditional structure. We extend a theorem of Guerre and Levy to Orlicz function spaces.
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Raynaud, Y. Finite representability ofl p(X) in Orlicz function spaces. Israel J. Math. 65, 197–213 (1989). https://doi.org/10.1007/BF02764860
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DOI: https://doi.org/10.1007/BF02764860