On the type constants with respect to systems of characters of a compact abelian group

Hinrichs, Aicke

Studia Mathematica, Tome 119 (1996), p. 231-243 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove that there exists an absolute constant c such that for any positive integer n and any system Φ of $2^n$ characters of a compact abelian group, $2^{-n/2} t_Φ(T) ≤ c n^{-1/2} t_n(T)$, where T is an arbitrary operator between Banach spaces, $t_Φ(T)$ is the type norm of T with respect to Φ and $t_n(T)$ is the usual Rademacher type-2 norm computed with n vectors. For the system of the first $2^n$ Walsh functions this is even true with c=1. This result combined with known properties of such type norms provides easy access to quantitative versions of the fact that a nontrivial type of a Banach space implies finite cotype and nontrivial type with respect to the Walsh system or the trigonometric system.

Détail

Publié le : 1996-01-01

Zbl 0855.46007

EUDML-ID : urn:eudml:doc:216275

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