The Dunford–Pettis property on tensor products
نویسندگان
چکیده
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...
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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...
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ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2001
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004101005175