Results 1 to 10 of about 425 (55)
The Szlenk Index and the Fixed Point Property under Renorming [PDF]
Fixed Point Theory and Applications, 2010 Assume that X is a Banach space such that its Szlenk index Sz(X) is less than or equal to the first infinite ordinal ω. We prove that X can be renormed in such a way that X with the resultant norm satisfies R(X)<2, where R(⋅) is the ...
T. Domínguez Benavides
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Banach spaces of bounded Szlenk index [PDF]
Studia Mathematica, 2007 For a countable ordinal a we denote by C_a the class of separable, reflexive Banach spaces whose Szlenk index and the Szlenk index of their dual are bounded by a. We show that each C_a admits a separable, reflexive universal space.
Odell, Edward +2 more
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Estimation of the Szlenk index of Banach Spaces via Schreier spaces [PDF]
Studia Mathematica, 2013 For each ordinal ...
Causey, Ryan
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Prescribed Szlenk index of separable Banach spaces [PDF]
Studia Mathematica, 2019 In a previous work, the first named author described the set $\cal P$ of all values of the Szlenk indices of separable Banach spaces. We complete this result by showing that for any integer $n$ and any ordinal $ $ in $\cal P$, there exists a separable Banach space $X$ such that the Szlenk of the dual of order $k$ of $X$ is equal to the first infinite ...
Causey, R, M, Lancien, Gilles
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Banach spaces of bounded Szlenk index II [PDF]
Fundamenta Mathematicae, 2009 For every $
Freeman, D. +3 more
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Szlenk indices of convex hulls [PDF]
, 2016 We study the general measures of non-compactness defined on subsets of a dual Banach space, their associated derivations and their $\omega$-iterates. We introduce the notions of convexifiable and sublinear measure of non-compactness and investigate the ...
Lancien, Gilles +2 more
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CONCERNING SUMMABLE SZLENK INDEX [PDF]
Glasgow Mathematical Journal, 2018 AbstractWe generalize the notion of summable Szlenk index from a Banach space to an arbitrary weak*-compact set. We prove that a weak*-compact set has summable Szlenk index if and only if its weak*-closed, absolutely convex hull does. As a consequence, we offer a new, short proof of a result from Draga and Kochanek [J. Funct. Anal. 271 (2016), 642–671]
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A new metric invariant for Banach spaces [PDF]
, 2009 We show that if the Szlenk index of a Banach space $X$ is larger than the first infinite ordinal $\omega$ or if the Szlenk index of its dual is larger than $\omega$, then the tree of all finite sequences of integers equipped with the hyperbolic distance ...
Baudier, F., Kalton, N. J., Lancien, G.
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Concerning $q$-summable Szlenk index [PDF]
Illinois Journal of Mathematics, 2018 For each ordinal $ $ and each $1\leqslant ...
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The Szlenk index of 𝐿_{𝑝}(𝑋) and 𝐴_{𝑝} [PDF]
Proceedings of the American Mathematical Society, 2022 Given a Banach space X X , a w ∗ w^* -compact subset of X ∗ X^* , and 1 > p > ∞ 1>p>\infty , we provide an optimal relationship between the Szlenk index of K K and the Szlenk index of ...
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