Embeddings of Banach Spaces Into Banach Lattices and the Gordon–Lewis Property

Embeddings of Banach Spaces Into Banach Lattices and the Gordon–Lewis Property In this paper we first show that if X is a Banach space and α is a left invariant crossnorm on l∞⊗X, then there is a Banach lattice L and an isometric embedding J of X into L, so that I ⊗ J becomes an isometry of l∞⊗αX onto l∞⊗m J(X). Here I denotes the identity operator on l∞ and l∞⊗m J(X) the canonical lattice tensor product. This result is originally due to G. Pisier (unpublished), but our proof is different. We then use this to prove the main results which characterize the Gordon–Lewis property GL and related structures in terms of embeddings into Banach lattices. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Embeddings of Banach Spaces Into Banach Lattices and the Gordon–Lewis Property

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2001 by Kluwer Academic Publishers
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1011845208065
Publisher site
See Article on Publisher Site

Abstract

In this paper we first show that if X is a Banach space and α is a left invariant crossnorm on l∞⊗X, then there is a Banach lattice L and an isometric embedding J of X into L, so that I ⊗ J becomes an isometry of l∞⊗αX onto l∞⊗m J(X). Here I denotes the identity operator on l∞ and l∞⊗m J(X) the canonical lattice tensor product. This result is originally due to G. Pisier (unpublished), but our proof is different. We then use this to prove the main results which characterize the Gordon–Lewis property GL and related structures in terms of embeddings into Banach lattices.

Journal

PositivitySpringer Journals

Published: Oct 3, 2004

References

  • The relation between volume ratios and new concepts of GL-constants
    Gordon, Y.; Junge, M.; Nielsen, N.J.
  • Hyperplane conjecture for quotient spaces of L p
    Junge, M.

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