Some remarks about embeddings of l 1 k in finite-dimensional spaces

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Abstract

The span X n of functions x i(t)=±1, i=1, ..., n, on a set T in the supremum norm is considered. It is proved, for example, that X n contains an isometric copy of l 1 k for k≧cM n 2 /n log n where M n is the Rademacher average of {x i} 1 n . This generalizes a result of Pisier for characters. The proof uses a new combinatorial tool.

Original languageEnglish
Pages (from-to)129-138
Number of pages10
JournalIsrael Journal of Mathematics
Volume43
Issue number2
DOIs
StatePublished - Jun 1982

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