An Asplund space with norming Markuševič basis that is not weakly compactly generated [PDF]
Advances in Mathematics, 2021 We construct an Asplund Banach space $\mathcal{X}$ with a norming Marku evi basis such that $\mathcal{X}$ is not weakly compactly generated. This solves a long-standing open problem from the early nineties, originally due to Gilles Godefroy. En route to the proof, we construct a peculiar example of scattered compact space, that also solves a ...
Hájek, Petr +3 more
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Smoothness in weakly compactly generated Banach spaces
Journal of Functional Analysis, 1983 AbstractIf X∗ is a weakly compactly generated (WCG) Banach space, then X admits an equivalent C1-smooth norm. If a WCG Banach space X admits a Ck-smooth function with bounded support, then X admits Ck-smooth partitions of unity.
Godefroy, G +3 more
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Projections in Weakly Compactly Generated Banach Spaces and Chang's Conjecture [PDF]
Journal of Applied Analysis, 2005 A \(WCG\) Banach space \(X\) is said to have \textit{few operators} if there is a projectional resolution of the identity \((P_\alpha)_{\omega \leq \alpha \leq \lambda}\) such that any operator \(T \colon X \to X\) is of the form \(P + S\), where \(P\) is in the strong closure of the linear span of countably many \(P_\alpha\)'s and \(S\) has a ...
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The McShane integral in weakly compactly generated spaces
Journal of Functional Analysis, 2010 Revised version.
Avilés, A. +2 more
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Inner characterizations of weakly compactly generated Banach spaces and their relatives
Journal of Mathematical Analysis and Applications, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fabian, M. +3 more
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Smoothness and its equivalents in weakly compactly generated Banach spaces
Journal of Functional Analysis, 1974 AbstractSome equivalent properties of the existence of Fréchet smooth norms in weakly compactly generated (WCG) Banach spaces are shown. Heredity of WCG property in such spaces is proved. The property of having a shrinking Markuševič basis is hereditary in all Banach spaces. Projections in WCG spaces and their duals are studied.
John, K, Zizler, V
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On one generalization of weakly compactly generated Banach spaces [PDF]
Studia Mathematica, 1981 openaire +4 more sources
A function space C(X) which is weakly Lindelöf but not weakly compactly generated [PDF]
Studia Mathematica, 1979 openaire +3 more sources
ON $M$-STRUCTURE AND WEAKLY COMPACTLY GENERATED BANACH SPACES [PDF]
Proceedings of the Edinburgh Mathematical Society, 2003 AbstractIt is well known that every non-reflexive $M$-ideal is weakly compactly generated (in short, WCG). We present a family of Banach spaces $\{V_{s}:0 \lt s \lt 1\}$ which are not WCG and such that every $V_{s}$ satisfies the inequality$$ \|\f\|\geq\|\pi\f\|+s\|\f-\pi\f\|\quad\forall\f\in V_{s}^{\ast\ast\ast}, $$where $\pi$ is the canonical ...
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On Equivalent Characterizations of Weakly Compactly Generated Banach Spaces
Rocky Mountain Journal of Mathematics, 1994 Let us consider the following nice Theorem. For a Banach space \(V\) the following assertions are equivalent: (a) \(V\) is weakly compactly generated (w.c.g.), (b) \(V\) is GSG and simultaneously a Vašák (i.e., weakly \(K\)-countable determined) space, and (c) \(V\) is GSG and moreover \((V^*,w^*)\) continuously injects into \(\Sigma(\Gamma)\) for some
Fabian, M., Whitfield, J.H.M.
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