Indecomposable Banach spaces

Abstract

This paper aims at describing Tim Gowers' contributions to Banach space theory that earned him the Fields medal in 1998. In particular, the construction of the Gowers-Maurey space, a Banach space not containing an unconditional basic sequence, is sketched as is the Gowers dichotomy theorem that led to the solution of the homogeneous Banach space problem. Moreover, Gowers' counterexamples to the hyperplane problem and the Schröder-Bernstein problem are discussed.
 The paper is an extended version of a talk given at Freie Universität Berlin in December 1999; hence the reference to the next millennium at the very end actually appeals to the present millennium. It should be accessible to anyone with a basic knowledge of functional analysis and of German.