The Dunford-Pettis property on tensor products

Details The Dunford-Pettis property on tensor products The Dunford-Pettis property on tensor products

2000-04-15

arxiv.org/abs/math/0004101v1

Mathematics

Functional Analysis

9 pages

Scientific paper

10.1017/S0305004101005175

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 $(c_0\hat{\otimes}_\pi c_0)^{**}$ fails the DPP. Since $(c_0\hat{\otimes}_\pi c_0)^{*}$ 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 $E\hat{\otimes}_\epsilon F$ has the DPP if and only if both $E$ and $F$ have the Schur property. Other results and examples are given.

Affiliated with

Also associated with

No associations

Rating

The Dunford-Pettis property on tensor products does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Dunford-Pettis property on tensor products, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Dunford-Pettis property on tensor products will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-588668