Abstract
The aim of the present paper is to estimate in a precise manner the integerk=k(p,m,n,∈) so that an arbitrarym-dimensional subspaceX of the spacel n p ;p>2, contains an (1+∈)-isomorph ofl k p . The main argument of the proof consists of a probabilistic selection which uses a lemma of Slepian. The same method also shows that any system of normalized functions inL p ;p≥2, which is equivalent to the unit vector basis ofl n p , contains, for any∈>0, a subsystem of sizeh proportional ton, which is (1+∈)-equivalent to the unit vector basis ofl h p .
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The authors were supported by Grant No. 87-0079 from BSF.
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Bourgain, J., Tzafriri, L. Embeddingl k p in subspaces ofL p forp>2. Israel J. Math. 72, 321–340 (1990). https://doi.org/10.1007/BF02773788
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DOI: https://doi.org/10.1007/BF02773788