Lattice-embedding scales ofL
p
spaces into orlicz spaces |
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Authors: | Francisco L Hernández Baltasar Rodriguez-Salinas |
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Institution: | (1) Dpto Análisis Matemático, Facultad de Matemáticas, Universidad Complutense, 28040 Madrid, Spain |
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Abstract: | We study the setP
X
of scalarsp such thatL
p
is lattice-isomorphically embedded into a given rearrangement invariant (r.i.) function spaceX0, 1]. Given 0<α≤β<∞, we construct a family of Orlicz function spacesX=L
F
0, 1], with Boyd indicesα andβ, whose associated setsP
X
are the closed intervals γ, β], for everyγ withα≤γ≤β. In particular forα>2, this proves the existence of separable 2-convex r.i. function spaces on 0,1] containing isomorphically scales ofL
p
-spaces for different values ofp. We also show that, in general, the associated setP
X
is not closed. Similar questions in the setting of Banach spaces with uncountable symmetric basis are also considered. Thus,
we construct a family of Orlicz spaces ℓ
F
(I), with symmetric basis and indices fixed in advance, containing ℓ
p
(Γ-subspaces for differentp’s and uncountable Λ⊂I. In contrast with the behavior in the countable case (Lindenstrauss and Tzafriri L-T1]), we show that the set of scalarsp for which ℓ
p
(Γ) is isomorphic to a subspace of a given Orlicz space ℓ
F
(I) is not in general closed.
Supported in part by DGICYT grant PB 94-0243. |
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Keywords: | |
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