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COMBINATORICA Bolyai Society Springer-Verlag
 

Summary: COMBINATORICA
Bolyai Society ­ Springer-Verlag
0209­9683/110/$6.00 c 2010 J´anos Bolyai Mathematical Society and Springer-Verlag
Combinatorica 30 (4) (2010) 359­385
DOI: 10.1007/s00493-010-2507-1
A NEW APPROACH TO THE RAMSEY-TYPE GAMES
AND THE GOWERS DICHOTOMY IN F-SPACES
GEORGE ANDROULAKIS, STEPHEN J. DILWORTH*,
NIGEL J. KALTON
Received May 19, 2008
We give a new approach to the Ramsey-type results of Gowers on block bases in Banach
spaces and apply our results to prove the Gowers dichotomy in F-spaces.
1. Introduction
Our aim in this note is to establish the Gowers dichotomy [4] in a gen-
eral F-space (complete metric linear space). We say that an F-space X is
hereditarily indecomposable if it is impossible to find two separated infinite-
dimensional closed subspaces V,W, i.e., such that V W = {0} and V +W
is closed (or equivalently that the natural projection from V +W onto V is
continuous). Our main result is that an F-space either contains an uncon-
ditional basic sequence or an infinite-dimensional HI subspace. In order to

  

Source: Androulakis, George - Department of Mathematics, University of South Carolina

 

Collections: Mathematics