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Can anyone tell me if the Dunford-Pettis property is met for a separate refelxive Banach space $X$ with dual $X'$?

I would say that this is the case.

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    $\begingroup$ No. $\endgroup$ – Theo Bendit Jan 31 at 11:04
  • $\begingroup$ This means, that the $L^p$-Space (for $1<p<\infty$) do not have we Dunford Pettis property. Is there a similar statement for such rooms? $\endgroup$ – FuncAna09 Jan 31 at 15:55

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