Subspaces of Rearrangement-Invariant Spaces

Hernandez, Francisco L. ; Kalton, Nigel J.

Canadian journal of mathematics, Tome 48 (1996) no. 4, pp. 794-833

Résumé

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 2X 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 YN for some integer N.

Détail

DOI : 10.4153/CJM-1996-041-4

Mots-clés : 46B03

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