NDLI: Lattice-embedding scales ofL $^{ p }$ spaces into orlicz spaces

Content Provider	Springer Nature Link
Author	Hernández, Francisco L. Rodriguez Salinas, Baltasar
Copyright Year	1998
Abstract	We study the setP $_{ X }$ of scalarsp such thatL $^{ p }$ is lattice-isomorphically embedded into a given rearrangement invariant (r.i.) function spaceX[0, 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-T$_{1}$]), 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.
Starting Page	191
Ending Page	220
Page Count	30
File Format	PDF
ISSN	00212172
Journal	Israel Journal of Mathematics
Volume Number	104
Issue Number	1
e-ISSN	15658511
Language	English
Publisher	Springer-Verlag
Publisher Date	1998-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematics Algebra Group Theory and Generalizations Analysis Applications of Mathematics Mathematical and Computational Physics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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