Weakly Continuous Mappings on Banach Spaces with the Dunford-Pettis Property
نویسندگان
چکیده
منابع مشابه
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...
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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...
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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.
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We study the class of Dunford-Pettis sets in Banach lattices. In particular, we establish some sufficient conditions for which a Dunford-Pettis set is relatively weakly compact (resp. relatively compact).
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1993
ISSN: 0022-247X
DOI: 10.1006/jmaa.1993.1080