Displaying similar documents to “A new class of weakly countably determined Banach spaces”

A note on weakly Lindelöf determined Banach spaces

A. González, Vicente Montesinos (2009)

Czechoslovak Mathematical Journal

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We prove that weakly Lindelöf determined Banach spaces are characterized by the existence of a ``full'' projectional generator. Some other results pertaining to this class of Banach spaces are given.

Weakly countably determined spaces of high complexity

Antonio Avilés (2008)

Studia Mathematica

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We prove that there exist weakly countably determined spaces of complexity higher than coanalytic. On the other hand, we also show that coanalytic sets can be characterized by the existence of a cofinal adequate family of closed sets. Therefore the Banach spaces constructed by means of these families have at most coanalytic complexity.

A new class of weakly K -analytic Banach spaces

Sophocles Mercourakis, E. Stamati (2006)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we define and investigate a new subclass of those Banach spaces which are K -analytic in their weak topology; we call them strongly weakly K -analytic (SWKA) Banach spaces. The class of SWKA Banach spaces extends the known class of strongly weakly compactly generated (SWCG) Banach spaces (and their subspaces) and it is related to that in the same way as the familiar classes of weakly K -analytic (WKA) and weakly compactly generated (WCG) Banach spaces are related. We show...

Weak compactness and σ-Asplund generated Banach spaces

M. Fabian, V. Montesinos, V. Zizler (2007)

Studia Mathematica

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σ-Asplund generated Banach spaces are used to give new characterizations of subspaces of weakly compactly generated spaces and to prove some results on Radon-Nikodým compacta. We show, typically, that in the framework of weakly Lindelöf determined Banach spaces, subspaces of weakly compactly generated spaces are the same as σ-Asplund generated spaces. For this purpose, we study relationships between quantitative versions of Asplund property, dentability, differentiability, and of weak...

Some strongly bounded classes of Banach spaces

Pandelis Dodos, Valentin Ferenczi (2007)

Fundamenta Mathematicae

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We show that the classes of separable reflexive Banach spaces and of spaces with separable dual are strongly bounded. This gives a new proof of a recent result of E. Odell and Th. Schlumprecht, asserting that there exists a separable reflexive Banach space containing isomorphic copies of every separable uniformly convex Banach space.