Abstract
Given 0<α≤p≤β<∞, we construct Orlicz function spacesL F[0, 1] with Boyd indicesα andβ such thatL p is lattice isomorphic to a sublattice ofL F[0, 1]. Forp>2 this shows the existence of (non-trivial) separable r.i. spaces on [0, 1] containing an isomorphic copy ofL p. The discrete case of Orlicz spaces ℓF (I) containing an isomorphic copy of ℓp(Γ) for uncountable sets Γ ⊂I is also considered.
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Supported in part by DGICYT, grant PB91-0377.
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Hernández, F.L., Rodríguez-Salinas, B. Lattice-embeddingL p into Orlicz spaces. Israel J. Math. 90, 167–188 (1995). https://doi.org/10.1007/BF02783211
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DOI: https://doi.org/10.1007/BF02783211