1995/03/02 by Francisco L. Hernández, Hernandez, F. L., N. J. Kalton +1 · 1 citation
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #Approximation Theory and Sequence Spaces
paper · pdf · doi:10.48550/arxiv.math/9503211
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≠ L2. We also show that if Y is an order-continuous Banach lattice which contains no complemented sublattice lattice-isomorphic to ℓ2, X is an order-continuous Banach lattice so that ℓ2 is not complementably lattice finitely representable in X and X is isomorphic to a complemented subpace of Y then X is isomorphic to a complemented sublattice of YN for some integer N.