A discretized approach to W.T. Gowers' game
V. Kanellopoulos, K. Tyros
TL;DR
This paper presents a new proof of Gowers' theorem on block bases by translating it into a discrete setting and also establishes a Ramsey-type result for block sequences in normed spaces with Schauder bases.
Contribution
It introduces a discretized approach to Gowers' theorem and extends Ramsey theory to block sequences in normed linear spaces.
Findings
Alternative proof of Gowers' theorem via discrete analogue
Ramsey-type result for k-tuples of block sequences
Extension to normed linear spaces with Schauder bases
Abstract
We give an alternative proof of W. T. Gowers' theorem on block bases by reducing it to a discrete analogue on specific countable nets. We also give a Ramsey type result on k-tuples of block sequences in a normed linear space with a Schauder basis.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Mathematical Dynamics and Fractals · Computability, Logic, AI Algorithms