A study of conditional spreading sequences

Argyros, Spiros A.; Motakis, Pavlos; Sarı, Bünyamin

doi:10.1016/j.jfa.2017.04.009

Cited by 12 publications

(6 citation statements)

References 18 publications

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“…We will use these facts without mention. More information about ESA sequences can be found in [5] and [1].…”

Section: Embedding Into Banach Spaces With Esa Basesmentioning

confidence: 99%

A Coding of Bundle Graphs and Their Embeddings Into Banach Spaces

Swift

2018

Mathematika

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The purpose of this article is to generalize some known characterizations of Banach space properties in terms of graph preclusion. In particular, it is shown that superreflexivity can be characterized by the non-equi-bi-Lipschitz embeddability of any family of bundle graphs generated by a nontrivial finitely-branching bundle graph. It is likewise shown that asymptotic uniform convexifiability can be characterized within the class of reflexive Banach spaces with an unconditional asymptotic structure by the non-equi-bi-Lipschitz embeddability of any family of bundle graphs generated by a nontrivial ℵ 0 -branching bundle graph. The best known distortions are recovered. For the specific case of L 1 , it is shown that every countably-branching bundle graph bi-Lipschitzly embeds into L 1 with distortion no worse than 2.

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“…We will use these facts without mention. More information about ESA sequences can be found in [5] and [1].…”

Section: Embedding Into Banach Spaces With Esa Basesmentioning

confidence: 99%

A Coding of Bundle Graphs and Their Embeddings Into Banach Spaces

Swift

2018

Mathematika

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“…Remark 4.4. Let us mention that, more generally, it is proved in [2] that for any conditional normalized spreading sequence (e n ) ∞ n=1 , there exists a quasi-reflexive Banach space X of order 1 with a normalized basis (…”

Section: The General Resultsmentioning

confidence: 99%

On the Coarse Geometry of James Spaces

Lancien¹,

Petitjean²,

Procházka³

2019

Can. Math. Bull.

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In this note we prove that the Kalton interlaced graphs do not equi-coarsely embed into the James space J nor into its dual J * . It is a particular case of a more general result on the non equicoarse embeddability of the Kalton graphs into quasi-reflexive spaces with a special asymptotic stucture. This allows us to exhibit a coarse invariant for Banach spaces, namely the non equi-coarse embeddability of this family of graphs, which is very close to but different from the celebrated property Q of Kalton. We conclude with a remark on the coarse geometry of the James tree space J T and of its predual.

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“…Proof. Proposition 7.4 from [3] says the result holds, provided that the sequence (e i ) i is equivalent to its convex block sequences and not equivalent to the summing basis of c 0 . Both of these properties follow from (1).…”

Section: A Brief Discussion Of Basic Conceptsmentioning

confidence: 98%

Strategically reproducible bases and the factorization property

Lechner,

Motakis,

Müller

et al. 2018

Preprint

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We introduce the concept of strategically reproducible bases in Banach spaces and show that operators which have large diagonal with respect to strategically reproducible bases are factors of the identity. We give several examples of classical Banach spaces in which the Haar system is strategically reproducible: multi-parameter Lebesgue spaces, mixed-norm Hardy spaces and most significantly the space L 1 . Moreover, we show the strategical reproducibility is inherited by unconditional sums.

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A study of conditional spreading sequences

Cited by 12 publications

References 18 publications

A Coding of Bundle Graphs and Their Embeddings Into Banach Spaces

A Coding of Bundle Graphs and Their Embeddings Into Banach Spaces

On the Coarse Geometry of James Spaces

Strategically reproducible bases and the factorization property

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