Geodesic
Some Ramsey type theorems for normed and quasinormed spaces
C. Ward Henson ;  ;  ;  ; 
Studia Mathematica, Tome 124 (1997) no. 1, pp. 81-100
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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 $L_p[0,1]$ for each 0 p 1. Some consequences for nonstandard topological vector spaces are derived.
DOI : 10.4064/sm-124-1-81-100
Keywords: normed space, Banach space, quasinormed and quasi-Banach space, p-norm, biorthogonal sequence, uniformly independent sequence, irreducible sequence, Ramsey's Theorem, nonstandard analysis 
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C. Ward Henson;  ;  ;  ;  . Some Ramsey type theorems for normed and quasinormed spaces. Studia Mathematica, Tome 124 (1997) no. 1, pp. 81-100. doi: 10.4064/sm-124-1-81-100

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