András Zsák

Banach spaces of bounded Szlenk index

Abstract. 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 each Cα is analytic in the Effros-Borel structure of subspaces of C[0, 1].

Coefficient quantization for frames in Banach spaces

Let (ei) be a fundamental system of a Banach space. We consider the problem of approximating linear combinations of elements of this system by linear combinations using quantized coefficients. We will concentrate on systems which are possibly redundant. Our model for this situation will be frames in Banach spaces.

Dichotomy theorems for random matrices and closed ideals of operators on (⊕n=1∞ℓ1n)co

We prove two dichotomy theorems about sequences of operators into

The algebra of bounded linear operators on ℓp ⊕ ℓq has infinitely many closed ideals

L_1

ON THE STRUCTURE OF ASYMPTOTIC p SPACES

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

Banach spaces of bounded Szlenk index II

\ell_1^k

\ell_p\oplus\ell_q

(k\in\mathbb N

has infinitely many closed ideals

) or uniformly approximately factor through

A new infinite game in Banach spaces with applications

\mathrm{c}_0