Banach spaces whose duals contain $l\sb{1}(\Gamma )$ with applications to the study of dual $L\sb{1}(\mu )$ spaces
نویسندگان
چکیده
منابع مشابه
ON BANACH SPACES WHOSE DUALS ARE ISOMORPHIC TO l1(Γ)
In this paper we present new characterizations of Banach spaces whose duals are isomorphic to l1(Γ), extending results of Stegall, Lewis-Stegall and Cilia-D’Anna-Gutiérrez.
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We prove that a Banach space admitting an equivalent WUR norm is an Asplund space. Some related dual renormings are also presented. It is a well-known result that a Banach space whose dual norm is Fréchet differentiable is reflexive. Also if the the third dual norm is Gâteaux differentiable the space is reflexive. For these results see e.g. [2], p.33. Similarly, by the result of [9], if the sec...
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Let E and F be Banach spaces. We say that E is F -saturated if every infinite dimensional closed subspace of E contains an isomorphic copy of F . In [2], it is shown that there exists a c0-saturated Banach space with an unconditional basis whose dual contains an isomorphic copy of l2. In this note, we give an example where the dual situation occurs. It is shown that there is a Banach space with...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1973
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1973-0315404-3