Another proof of a Gowers theorem

2012/09/27 by Jesús E. Nieto, Nieto, Jesús E.
Mathematics · #05D10 #46B45 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05D10 #msc:46B45

paper · pdf · doi:10.48550/arxiv.1209.6103

This paper has been withdrawn by the author due to a wrong argument used in the proof of the main result

arxiv created 2012/11/04 · arxiv updated 2012/11/06

Abstract

W. T. Gowers proved that every Lipschitz function from the unit sphere of the Banach space c₀ to ℝ is oscilation stable. His proof uses a result about finite partitions of the set FIN_k of finitely supported functions p from ℕ to \0,1,...,k\ with k in Im(p). Every known proof of this fact uses methods of topological dynamics on the space βℕ of ultrafilters on ℕ. We give a purely combinatorial proof of this result avoiding the use of ultrafilters.

Related

• Finite forms of Gowers' Theorem on the oscillation stability of c₀
• An infinite-dimensional version of Gowers' \FIN_{\± k}\n theorem
• Oscillation stability by the Carlson-Simpson theorem
• Combinatorial proofs of Gowers' FIN_k and FIN_k^± theorem
• Local vanishing mean oscillation