Reflexivity and the Grothendieck property for positive tensor products of Banach lattices-I

Reflexivity and the Grothendieck property for positive tensor products of Banach lattices-I Let X be a Banach lattice and p, p′ be real numbers such that 1 < p, p′<∞ and 1/p + 1/p′ = 1. Then $${\ell_p\hat{\otimes}_FX}$$ (respectively, $${\ell_p\tilde{\otimes}_{i}X}$$ ), the Fremlin projective (respectively, the Wittstock injective) tensor product of ℓ p and X, has reflexivity or the Grothendieck property if and only if X has the same property and each positive linear operator from ℓ p (respectively, from ℓ p′) to X* (respectively, to X**) is compact. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Reflexivity and the Grothendieck property for positive tensor products of Banach lattices-I

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Publisher
SP Birkhäuser Verlag Basel
Copyright
Copyright © 2009 by Birkhäuser Verlag Basel/Switzerland
Subject
Mathematics; Econometrics; Calculus of Variations and Optimal Control; Optimization; Potential Theory; Operator Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-009-0004-9
Publisher site
See Article on Publisher Site

Abstract

Let X be a Banach lattice and p, p′ be real numbers such that 1 < p, p′<∞ and 1/p + 1/p′ = 1. Then $${\ell_p\hat{\otimes}_FX}$$ (respectively, $${\ell_p\tilde{\otimes}_{i}X}$$ ), the Fremlin projective (respectively, the Wittstock injective) tensor product of ℓ p and X, has reflexivity or the Grothendieck property if and only if X has the same property and each positive linear operator from ℓ p (respectively, from ℓ p′) to X* (respectively, to X**) is compact.

Journal

PositivitySpringer Journals

Published: Feb 3, 2009

References

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