# The Radon-Nikodym Property for Tensor Products of Banach Lattices II

The Radon-Nikodym Property for Tensor Products of Banach Lattices II Let φ be an Orlicz function that has a complementary function φ* and let ℓ φ be an Orlicz sequence space. We prove two results in this paper. Result 1: $$\ell_\varphi\hat{\otimes}_F X$$ , the Fremlin projective tensor product of ℓ φ with a Banach lattice X, has the Radon-Nikodym property if and only if both ℓ φ and X have the Radon-Nikodym property. Result 2: $$\ell_\varphi\tilde{\otimes}_i X$$ , the Wittstock injective tensor product of ℓ φ with a Banach lattice X, has the Radon-Nikodym property if and only if both ℓ φ and X have the Radon-Nikodym property and each positive continuous linear operator from h φ* to X is compact. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# The Radon-Nikodym Property for Tensor Products of Banach Lattices II

, Volume 12 (1) – Oct 29, 2007
10 pages

Publisher
Springer Journals
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.
10.1007/s11117-007-2152-0
Publisher site
See Article on Publisher Site

### Abstract

Let φ be an Orlicz function that has a complementary function φ* and let ℓ φ be an Orlicz sequence space. We prove two results in this paper. Result 1: $$\ell_\varphi\hat{\otimes}_F X$$ , the Fremlin projective tensor product of ℓ φ with a Banach lattice X, has the Radon-Nikodym property if and only if both ℓ φ and X have the Radon-Nikodym property. Result 2: $$\ell_\varphi\tilde{\otimes}_i X$$ , the Wittstock injective tensor product of ℓ φ with a Banach lattice X, has the Radon-Nikodym property if and only if both ℓ φ and X have the Radon-Nikodym property and each positive continuous linear operator from h φ* to X is compact.

### Journal

PositivitySpringer Journals

Published: Oct 29, 2007

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