A proof of W. T. Gowers' 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 | References | Similar Articles | Additional Information

Abstract: W. T. Gowers' theorem asserts that for every Lipschitz function and , there exists an infinite-dimensional subspace of such that the oscillation of on is at most . 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