English

A simple, combinatorial proof of Gowers Dichotomy for Banach Spaces

Functional Analysis 2023-07-31 v4 Combinatorics

Abstract

In this paper we present a simple proof of Gowers Dichotomy which states that every infinite dimensional Banach Space has a subspace which either contains an unconditional basic sequence or is hereditarily indecomposable. Our approach is purely combinatorial and mainly based on work of Ellentuck, Galvin and Prikry in infinite Ramsey theory.

Keywords

Cite

@article{arxiv.2106.10728,
  title  = {A simple, combinatorial proof of Gowers Dichotomy for Banach Spaces},
  author = {Ryszard Frankiewicz and Sławomir Kusiński},
  journal= {arXiv preprint arXiv:2106.10728},
  year   = {2023}
}