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A CHARACTERIZATION OF SUBSPACES OF WEAKLY COMPACTLY GENERATED BANACH SPACES
Journal of the London Mathematical Society, 2004The main result goes as follows: A Banach space \(X\) is a subspace of a weakly compactly generated Banach space if and only if, for every \(\varepsilon> 0\), \(X\) can be covered by a countable collection of bounded closed convex symmetric sets where the weak\(^*\) closure in \(X^{**}\) of each of them lies within the distance \(\varepsilon\) from \(X\
Fabian, M., Montesinos, V., Zizler, V.
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Strongly Asplund generated and strongly conditionally weakly compactly generated Banach spaces
Monatshefte für Mathematik, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lajara, Sebastián, Rodríguez, José
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On Weakly-Compactly Generated Asplund Banach spaces
The Quarterly Journal of Mathematics, 2004In [Proc. Lond. Math. Soc. 75, No. 3, 619--640 (1997; Zbl 0909.46011)], \textit{A. Moltó, J. Orihuela} and \textit{S. Troyanski} have proposed a new approach to renorming of Banach spaces which is based on the following linking property. Let \(X\) be a set and \(\tau_1,\tau_2\) be topologies on it.
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Weakly compactly generated Banach spaces and the strong law of large numbers
Journal of Theoretical Probability, 1994The author studies the structure of a random variable, taking values in a Banach space, such that independent copies of the random variable satisfy the strong law of large numbers. If the Banach space coincides with the closed linear span of a compact in the weak topology, then the random variable can be represented as sum of a random variable with ...
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Weakly compactly generated locally convex spaces
Mathematical Proceedings of the Cambridge Philosophical Society, 1977AbstractLocally convex spaces which are generated by a weakly compact subset (or a sequence of weakly compact subsets) and their subspaces are studied. Various characterizations and the permanence properties of these spaces are obtained. Certain results valid for weakly compactly generated Banach spaces are extended.
Hunter, Richard J., Lloyd, John
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Weakly Compactly Generated Spaces
2010In this chapter we study weakly compact operators and the related class of Banach spaces that are generated by weakly compact sets (i.e., weakly compactly generated spaces, in short WCG spaces). We focus on their decomposition properties, renormings, and on the topological properties of their dual spaces.
Marián Fabian +4 more
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Weakly compactly generated spaces and their relatives III
2022Antonio José Guirao +2 more
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Innovations in research and clinical care using patient‐generated health data
Ca-A Cancer Journal for Clinicians, 2020H S L Jim +2 more
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