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- Edward Odell, TH . SCHLUMPRECHT, András Zsák
- 2008

For a countable ordinal α we denote by Cα the class of separable, reflexive Banach spaces whose Szlenk index and the Szlenk index of their dual are bounded by α. We show that each Cα admits a separable, reflexive universal space. We also show that spaces in the class Cωα·ω embed into spaces of the same class with a basis. As a consequence we deduce that… (More)

In this paper we determine the closed operator ideals of the space F := (⊕ n∈N ` n 2 )

- TH . SCHLUMPRECHT, András Zsák
- 2007

Abstract. We prove that if X is a separable, reflexive space which is asymptotic lp for some 1 ≤ p ≤ ∞, then X embeds into a reflexive space Z having an asymptotic lp finite-dimensional decomposition. This result leads to an intrinsic characterization of subspaces of spaces with an asymptotic lp FDD. More general results of this type are also obtained. As a… (More)

The James–Schreier spaces Vp, where 1 6 p < ∞, were recently introduced by Bird and Laustsen [5] as an amalgamation of James’ quasi-reflexive Banach space on the one hand and Schreier’s Banach space giving a counterexample to the Banach–Saks property on the other. The purpose of this note is to answer some questions left open in [5]. Specifically, we prove… (More)

- Edward Odell, TH . SCHLUMPRECHT, András Zsák
- 2006

(if p = ∞ we use the c0-norm max ‖xi‖). A coordinate-free version of this notion is as follows [MMT]. Let X be an arbitrary Banach space, and let cof(X) denote the set of all closed subspaces of X having finite codimension. We say X is asymptotic lp if there exists C < ∞ so that ∀n ∈ N ∃Y1 ∈ cof(X) ∀y1 ∈ SY1 (unit sphere of Y1) (1) ∃Y2 ∈ cof(X) ∀y2 ∈ SY2 ..… (More)

- FLORENT BAUDIER, Dan Freeman, TH . SCHLUMPRECHT, András Zsák
- 2014

The Lipschitz geometry of segments of the infinite Hamming cube is studied. Tight estimates on the distortion necessary to embed the segments into spaces of continuous functions on countable compact metric spaces are given. As an application, the first nontrivial lower bounds on the C(K)distortion of important classes of separable Banach spaces, where K is… (More)

- N. J. Laustsen, Edward Odell, Th Schlumprecht, András Zsák
- 2010

We prove two dichotomy theorems about sequences of operators into L1 given by random matrices. In the second theorem we assume that the entries of each random matrix form a sequence of independent, symmetric random variables. Then the corresponding sequence of operators either uniformly factor the identity operators on `1 (k ∈ N) or uniformly approximately… (More)

- N. J. Laustsen, Edward Odell, Thomas Schlumprecht, András Zsák
- J. London Math. Society
- 2012

- Edward Odell, TH . SCHLUMPRECHT, András Zsák
- 2008

Let X be a separable infinite-dimensional Banach space, and let A be a set of normalized sequences in X . We can consider a two-player game in X each move of which consists of player S (subspace chooser) selecting some element Y from the set cof(X) of finite-codimensional subspaces of X , and P (point chooser) responding by selecting a vector y from the… (More)

- Edward Odell, András Zsák
- 2006

We prove that if X is a separable, reflexive space which is asymptotic `p for some 1 ≤ p ≤ ∞, then X embeds into a reflexive space Z having an asymptotic `p finite-dimensional decomposition. This result leads to an intrinsic characterization of subspaces of spaces with an asymptotic `p FDD. More general results of this type are also obtained. As a… (More)