Some Ramsey type theorems for normed and quasinormed spaces
Henson, C. ; Kalton, Nigel ; Peck, N. ; Tereščák, Ignác ; Zlatoš, Pavol
Studia Mathematica, Tome 122 (1997), p. 81-100 / Harvested from The Polish Digital Mathematics Library
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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 Lp[0,1] for each 0 < p < 1. Some consequences for nonstandard topological vector spaces are derived.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:216398 
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Henson, C.; Kalton, Nigel; Peck, N.; Tereščák, Ignác; Zlatoš, Pavol. Some Ramsey type theorems for normed and quasinormed spaces. Studia Mathematica, Tome 122 (1997) pp. 81-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv124i1p81bwm/

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