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The Dunford-Pettis property on tensor products | Manuel González
; Joaqu’{i}n M. Gutiérrez
; | Date: |
15 Apr 2000 | Subject: | Functional Analysis MSC-class: 46B20; 46B28 | math.FA | Abstract: | We show that, in some cases, the projective and the injective tensor products of two Banach spaces do not have the Dunford-Pettis property (DPP). As a consequence, we obtain that $(c_0hat{otimes}_pi c_0)^{**}$ fails the DPP. Since $(c_0hat{otimes}_pi c_0)^{*}$ does enjoy it, this provides a new space with the DPP whose dual fails to have it. We also prove that, if $E$ and $F$ are ${mathscr L}_1$-spaces, then $Ehat{otimes}_epsilon F$ has the DPP if and only if both $E$ and $F$ have the Schur property. Other results and examples are given. | Source: | arXiv, math.FA/0004101 | Services: | Forum | Review | PDF | Favorites |
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