منابع مشابه
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...
متن کاملThe Alternative Dunford-pettis Property in C∗-algebras and Von Neumann Preduals
A Banach space X is said to have the alternative Dunford-Pettis property if, whenever a sequence xn → x weakly in X with ‖xn‖ → ‖x‖, we have ρn(xn) → 0 for each weakly null sequence (ρn) in X∗. We show that a C∗-algebra has the alternative Dunford-Pettis property if and only if every one of its irreducible representations is finite dimensional so that, for C∗-algebras, the alternative and the u...
متن کاملThe Alternative Dunford–pettis Property, Conjugations and Real Forms of C∗-algebras
Let τ be a conjugation, alias a conjugate linear isometry of order 2, on a complex Banach space X and let Xτ be the real form of X of τ -fixed points. In contrast to the Dunford–Pettis property, the alternative Dunford–Pettis property need not lift from Xτ to X. If X is a C*-algebra it is shown that Xτ has the alternative Dunford–Pettis property if and only if X does and an analogous result is ...
متن کاملSome 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.
متن کاملBanach 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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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1990
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-97-1-59-64