On vector-valued inequalities for Sidon sets and sets of interpolation
Kalton, N.
Colloquium Mathematicae, Tome 66 (1993), p. 233-244 / Harvested from The Polish Digital Mathematics Library
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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 Lp-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 (I0-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.

Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:210187 
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Kalton, N. On vector-valued inequalities for Sidon sets and sets of interpolation. Colloquium Mathematicae, Tome 66 (1993) pp. 233-244. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv64i2p233bwm/

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