Subspaces of Rearrangement-invariant Spaces
نویسندگان
چکیده
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, oo) which is/7-convex for some/? > 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>2byX^L2. We also show that if Y is an order-continuous Banach lattice which contains no complemented sublattice lattice-isomorphic to l^ Xis an order-continuous Banach lattice so that £2 is n o t 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 for some integer N.
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