On the Dunford-Pettis property of tensor product spaces
Ioana Ghenciu
Colloquium Mathematicae, Tome 122 (2011), p. 221-231 / Harvested from The Polish Digital Mathematics Library
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We give sufficient conditions on Banach spaces E and F so that their projective tensor product E⊗πF and the duals of their projective and injective tensor products do not have the Dunford-Pettis property. We prove that if E* does not have the Schur property, F is infinite-dimensional, and every operator T:E* → F** is completely continuous, then (E⊗ϵF)* does not have the DPP. We also prove that if E* does not have the Schur property, F is infinite-dimensional, and every operator T: F** → E* is completely continuous, then (E⊗πF)*≃L(E,F*) does not have the DPP.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:284214 
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Ioana Ghenciu. On the Dunford-Pettis property of tensor product spaces. Colloquium Mathematicae, Tome 122 (2011) pp. 221-231. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-2-7/