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Some Ramsey type theorems for normed and quasinormed spaces

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Henson C. W., Kalton N. J., Tenney Peck N., Tereščák I., Zlatoš P.

Studia Mathematica

1997

tom 124

nr 1

81-100

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.

Ograniczanie wyników

1 Studia Mathematica

1 Henson C. W.

1 Kalton N. J.

1 Tenney Peck N.

1 Tereščák I.

1 Zlatoš P.

1 1997

Wyniki wyszukiwania

Some Ramsey type theorems for normed and quasinormed spaces