On vector-valued inequalities for Sidon sets and sets of interpolation

Volume 64 / 1993

N. Kalton Colloquium Mathematicum 64 (1993), 233-244 DOI: 10.4064/cm-64-2-233-244

Abstract

Let E be a Sidon subset of the integers and suppose X is a Banach space. Then Pisier has shown that E-spectral polynomials with values in X behave like Rademacher sums with respect to $L_p$-norms. We consider the situation when X is a quasi-Banach space. For general quasi-Banach spaces we show that a similar result holds if and only if E is a set of interpolation ($I_0$-set). However, for certain special classes of quasi-Banach spaces we are able to prove such a result for larger sets. Thus if X is restricted to be "natural" then the result holds for all Sidon sets. We also consider spaces with plurisubharmonic norms and introduce the class of analytic Sidon sets.

Authors

  • N. Kalton

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