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- W2007231837 abstract "Abstract We prove a number of results concerning the embedding of a Banach lattice X into an r. i. space Y . For example we show that if Y is an r. i. space on [0, ∞) which is p -convex for some p > 2 and has nontrivial concavity then any Banach lattice X which is r -convex for some r > 2 and embeds into Y must embed as a sublattice. Similar conclusions can be drawn under a variety of hypotheses on Y ; if X is an r. i. space on [0, 1] one can replace the hypotheses of r -convexity for some r > 2 by X ≠ L 2 . We also show that if Y is an order-continuous Banach lattice which contains no complemented sublattice lattice-isomorphic to ℓ 2 X is an order-continuous Banach lattice so that ℓ 2 is not complementary lattice finitely representable in X and X is isomorphic to a complemented subspace of Y then X is isomorphic to a complemented sublattice of Y N for some integer N ." @default.
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- W2007231837 date "1996-08-01" @default.
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- W2007231837 title "Subspaces of Rearrangement-Invariant Spaces" @default.
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- W2007231837 doi "https://doi.org/10.4153/cjm-1996-041-4" @default.
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