A proof of W. T. Gowers’ $c_0$ theorem
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- by Vassilis Kanellopoulos PDF
- Proc. Amer. Math. Soc. 132 (2004), 3231-3242 Request permission
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.References
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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
- 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
- © Copyright 2004 American Mathematical Society
- 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
- MathSciNet review: 2073297