JEDNOSTKA NAUKOWA KATEGORII A+

# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

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

### Tom 118 / 1996

Studia Mathematica 118 (1996), 231-243 DOI: 10.4064/sm-118-3-231-243

#### Streszczenie

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.

#### Autorzy

• Aicke Hinrichs

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek