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Some Ramsey type theorems for normed and quasinormed spaces

C. Henson, Nigel Kalton, N. Peck, Ignác Tereščák, Pavol Zlatoš (1997)

Studia Mathematica

We prove that every bounded, uniformly separated sequence in a normed space contains a “uniformly independent” subsequence (see definition); the constants involved do not depend on the sequence or the space. The finite version of this result is true for all quasinormed spaces. We give a counterexample to the infinite version in L p [ 0 , 1 ] for each 0 < p < 1. Some consequences for nonstandard topological vector spaces are derived.

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