A simple, combinatorial proof of Gowers Dichotomy for Banach Spaces

Published 20 Jun 2021 in math.FA and math.CO | (2106.10728v4)

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.

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