Comparing gaussian and Rademacher cotype for operators on the space of continuous functions

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Abstract

We prove an abstract comparison principle which translates gaussian co-type into Rademacher cotype conditions and vice versa. More precisely, let 2 < q < ∞ and T : C(K) → F a continuous linear operator. (1) T is of gaussian cotype q if and only if (formula presented) for all sequences (xk)k∈N ⊂ C(K) with (||Txk||)nk=1 decreasing. (2) T is of Rademacher cotype q if and only if (formula presented) for all sequences (xk)k∈N ⊂ C(K) with (||Txk||)nk=1 decreasing. Our method allows a restriction to a fixed number of vectors and complements the corresponding results of Talagrand.

Original languageEnglish (US)
Pages (from-to)101-115
Number of pages15
JournalStudia Mathematica
Volume118
Issue number2
DOIs
StatePublished - 1996
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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