András Zsák

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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)
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)
(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)
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)
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)
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)