Results 21 to 30 of about 445 (75)

A new isomorphic (\ell_1) predual not isomorphic to a complemented subspace of a (C(K)) space

, 2012
An isomorphic (\ell_1)-predual space (X) is constructed such that neither (X) is isomorphic to a subspace of (c_0), nor (C(\omega^\omega)) is isomorphic to a subspace of (X).
Gasparis, Ioannis
core   +1 more source

An alternate description of the Szlenk index with applications [PDF]

Illinois Journal of Mathematics, 2015
We discuss an alternate method for computing the Szlenk index of an arbitrary $w^*$ compact subset of the dual of a Banach space. We discuss consequences of this method as well as offer simple, alternative proofs of a number of results already found in the literature.
openaire   +4 more sources

On strong asymptotic uniform smoothness and convexity

, 2017
We introduce the notions of strong asymptotic uniform smoothness and convexity. We show that the injective tensor product of strongly asymptotically uniformly smooth spaces is asymptotically uniformly smooth.
García-Lirola, Luis, Raja, Matías
core   +1 more source

Compact spaces of Szlenk index ω

Journal of Mathematical Analysis and Applications, 2012
AbstractThe Szlenk index has found many applications in the isomorphic theory of Banach spaces. Its definition is based in some kind of interplay between a weak topology and the norm metric with not much care on the linear structure. There is no obstacle to consider the notion of Szlenk index in more general settings. In this paper we study the compact
openaire   +1 more source

Amalgamations of classes of Banach spaces with a monotone basis

, 2015
It was proved by Argyros and Dodos that, for many classes $ C $ of separable Banach spaces which share some property $ P $, there exists an isomorphically universal space that satisfies $ P $ as well.
Kurka, Ondřej
core   +1 more source

Direct sums and the Szlenk index

Journal of Functional Analysis, 2011
For $ $ an ordinal and ...
openaire   +3 more sources

Estimation of the Szlenk index of reflexive Banach spaces using generalized Baernstein spaces [PDF]

Fundamenta Mathematicae, 2015
arXiv admin note: text overlap with arXiv:1212 ...
openaire   +2 more sources

On Uniformly Convex and Uniformly Kadec-Klee Renomings [PDF]

, 1995
We give a new construction of uniformly convex norms with a power type modulus on super-reflexive spaces based on the notion of dentability index. Furthermore, we prove that if the Szlenk index of a Banach space is less than or equal to ω (first infinite
Lancien, Gilles
core  

A short calculation of the Szlenk index of spaces of continuous functions

, 2023
We provide a short calculation of the Szlenk index of $C(K)$ spaces using the Grasberg norm.
openaire   +2 more sources

Asplund operators and the Szlenk index

, 2010
For $ $ an ordinal, we investigate the class $\mathscr{SZ}_ $ consisting of all operators whose Szlenk index is an ordinal not exceeding $ ^ $. We show that each class $\mathscr{SZ}_ $ is a closed operator ideal and study various operator ideal properties for these classes.
openaire   +2 more sources