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Proceedings of the American Mathematical Society

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A proof of W. T. Gowers' $c_0$ theorem


Author: Vassilis Kanellopoulos
Journal: Proc. Amer. Math. Soc. 132 (2004), 3231-3242
MSC (2000): Primary 46B45, 46T20
DOI: https://doi.org/10.1090/S0002-9939-04-07320-4
Published electronically: June 16, 2004
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Abstract: W. T. Gowers' $c_0$ theorem asserts that for every Lipschitz function $F: S_{c_0} \to \mathbb{R} $ and $\varepsilon > 0$, there exists an infinite-dimensional subspace $Y$ of $c_0$ such that the oscillation of $F$ on $S_Y$ is at most $\varepsilon$. The proof of this theorem has been reduced by W. T. Gowers to the proof of a new Ramsey type theorem. Our aim is to present a proof of the last result.


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Additional Information

Vassilis Kanellopoulos
Affiliation: Department of Mathematics, National Technical University of Athens, Athens 15780, Greece
Email: bkanel@math.ntua.gr

DOI: https://doi.org/10.1090/S0002-9939-04-07320-4
Keywords: Lipschitz functions, compact semigroups, idempotents, ultrafilters, variable words
Received by editor(s): February 26, 2003
Received by editor(s) in revised form: March 23, 2003, and June 13, 2003
Published electronically: June 16, 2004
Additional Notes: Partially supported by Thales program of NTUA
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2004 American Mathematical Society