# Some Ramsey type theorems for normed and quasinormed spaces

C. Henson; Nigel Kalton; N. Peck; Ignác Tereščák; Pavol Zlatoš

Studia Mathematica (1997)

- Volume: 124, Issue: 1, page 81-100
- ISSN: 0039-3223

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topHenson, C., et al. "Some Ramsey type theorems for normed and quasinormed spaces." Studia Mathematica 124.1 (1997): 81-100. <http://eudml.org/doc/216398>.

@article{Henson1997,

abstract = {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.},

author = {Henson, C., Kalton, Nigel, Peck, N., Tereščák, Ignác, Zlatoš, Pavol},

journal = {Studia Mathematica},

keywords = {normed space; Banach space; quasinormed and quasi-Banach space; p-norm; biorthogonal sequence; uniformly independent sequence; irreducible sequence; Ramsey's Theorem; nonstandard analysis; -separated; -independent; quasinormed spaces},

language = {eng},

number = {1},

pages = {81-100},

title = {Some Ramsey type theorems for normed and quasinormed spaces},

url = {http://eudml.org/doc/216398},

volume = {124},

year = {1997},

}

TY - JOUR

AU - Henson, C.

AU - Kalton, Nigel

AU - Peck, N.

AU - Tereščák, Ignác

AU - Zlatoš, Pavol

TI - Some Ramsey type theorems for normed and quasinormed spaces

JO - Studia Mathematica

PY - 1997

VL - 124

IS - 1

SP - 81

EP - 100

AB - 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.

LA - eng

KW - normed space; Banach space; quasinormed and quasi-Banach space; p-norm; biorthogonal sequence; uniformly independent sequence; irreducible sequence; Ramsey's Theorem; nonstandard analysis; -separated; -independent; quasinormed spaces

UR - http://eudml.org/doc/216398

ER -

## References

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- [13] E. M. Stein and N. J. Weiss, On the convergence of Poisson integrals, Trans. Amer. Math. Soc. 140 (1969), 35-54. Zbl0182.10801

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