Geodesic
On the type constants with respect to systems of characters of a compact abelian group
Studia Mathematica, Tome 118 (1996) no. 3, pp. 231-243

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-118-3-231-243

Aicke Hinrichs 1

1 
@article{10_4064_sm_118_3_231_243,
     author = {Aicke Hinrichs},
     title = {On the type constants with respect to systems of characters of a compact abelian group},
     journal = {Studia Mathematica},
     pages = {231--243},
     publisher = {mathdoc},
     volume = {118},
     number = {3},
     year = {1996},
     doi = {10.4064/sm-118-3-231-243},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-118-3-231-243/}
}
TY  - JOUR
AU  - Aicke Hinrichs
TI  - On the type constants with respect to systems of characters of a compact abelian group
JO  - Studia Mathematica
PY  - 1996
SP  - 231
EP  - 243
VL  - 118
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm-118-3-231-243/
DO  - 10.4064/sm-118-3-231-243
LA  - en
ID  - 10_4064_sm_118_3_231_243
ER  - 
%0 Journal Article
%A Aicke Hinrichs
%T On the type constants with respect to systems of characters of a compact abelian group
%J Studia Mathematica
%D 1996
%P 231-243
%V 118
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm-118-3-231-243/
%R 10.4064/sm-118-3-231-243
%G en
%F 10_4064_sm_118_3_231_243
Aicke Hinrichs. On the type constants with respect to systems of characters of a compact abelian group. Studia Mathematica, Tome 118 (1996) no. 3, pp. 231-243. doi: 10.4064/sm-118-3-231-243

Cité par Sources :