# Dunford-Pettis for Banach-Spaces

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.

• No. – Theo Bendit Jan 31 at 11:04
• 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? – FuncAna09 Jan 31 at 15:55