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Subspaces of Rearrangement-Invariant Spaces

Published online by Cambridge University Press:  20 November 2018

Francisco L. Hernandez  and
Nigel J. Kalton
Francisco L. Hernandez
Affiliation:
Facultad de Matematicas Universidad Complutense28040 Madrid Spain, e-mail: [email protected]
Nigel J. Kalton
Affiliation:
Department of Mathematics University of Missouri Columbia, Missouri 65211 U.S.A., e-mail: [email protected]
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Abstract

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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 ℓ2X is an order-continuous Banach lattice so that ℓ2 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.

Keywords

46B03
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 4 , 01 August 1996 , pp. 794 - 833
Copyright
Copyright © Canadian Mathematical Society 1996

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