The hereditary Dcnford-Pettis property on $C(K,E)$

The Dunford-pettis Property on Tensor Products

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 (c0⊗̂πc0)∗∗ fails the DPP. Since (c0⊗̂πc0)∗ 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 L1-spaces, then E⊗̂ǫF has the DPP if and only if both E and...

Some Remarks on the Dunford-pettis Property

Let A be the disk algebra, Ω be a compact Hausdorff space and μ be a Borel measure on Ω. It is shown that the dual of C(Ω, A) has the Dunford-Pettis property. This proved in particular that the spaces L(μ,L/H 0 ) and C(Ω, A) have the Dunford-Pettis property.

The Alternative Dunford-pettis Property on Projective Tensor Products

In 1953 A. Grothendieck introduced the property known as Dunford-Pettis property [18]. A Banach space X has the Dunford-Pettis property (DPP in the sequel) if whenever (xn) and (ρn) are weakly null sequences in X and X∗, respectively, we have ρn(xn) → 0. It is due to Grothendieck that every C(K )-space satisfies the DPP. Historically, were Dunford and Pettis who first proved that L1(μ) satisfie...

Banach lattices with weak Dunford-Pettis property

We introduce and study the class of weak almost Dunford-Pettis operators. As an application, we characterize Banach lattices with the weak Dunford-Pettis property. Also, we establish some sufficient conditions for which each weak almost Dunford-Pettis operator is weak Dunford-Pettis. Finally, we derive some interesting results. Keywords—eak almost Dunford-Pettis operator, almost DunfordPettis o...

Duality Property for Positive Weak Dunford-Pettis Operators