Comparing gaussian and Rademacher cotype for operators on the space of continuous functions
Studia Mathematica, Tome 118 (1996) no. 2, pp. 101-115
We prove an abstract comparison principle which translates gaussian cotype into Rademacher cotype conditions and vice versa. More precisely, let 2 q ∞ and T: C(K) → F a continuous linear operator. (1) T is of gaussian cotype q if and only if $(∑_k ((∥Tx_k∥_F)/(√log(k+1)))^q)^{1/q} ≤ c ∥ ∑_k ɛ_{k} x_{k} ∥_{L_{2}(C(K))}$, for all sequences $(x_k)_{k∈ℕ} ⊂ C(K)$ with $(∥Tx_k∥)_{k=1}^n$ decreasing. (2) T is of Rademacher cotype q if and only if $(∑_k (∥Tx_k∥_{F} √((log(k+1))^q) )^{1/q} ≤ c ∥∑_k g_{k}x_{k}∥_{L_2(C(K))}$, for all sequences $(x_k)_{k∈ℕ} ⊂ C(K)$ with $(∥Tx_k∥)_{k=1}^n$ decreasing. Our method allows a restriction to a fixed number of vectors and complements the corresponding results of Talagrand.
@article{10_4064_sm_118_2_101_115,
author = {Marius Junge},
title = {Comparing gaussian and {Rademacher} cotype for operators on the space of continuous functions},
journal = {Studia Mathematica},
pages = {101--115},
year = {1996},
volume = {118},
number = {2},
doi = {10.4064/sm-118-2-101-115},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-118-2-101-115/}
}
TY - JOUR AU - Marius Junge TI - Comparing gaussian and Rademacher cotype for operators on the space of continuous functions JO - Studia Mathematica PY - 1996 SP - 101 EP - 115 VL - 118 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-118-2-101-115/ DO - 10.4064/sm-118-2-101-115 LA - en ID - 10_4064_sm_118_2_101_115 ER -
%0 Journal Article %A Marius Junge %T Comparing gaussian and Rademacher cotype for operators on the space of continuous functions %J Studia Mathematica %D 1996 %P 101-115 %V 118 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4064/sm-118-2-101-115/ %R 10.4064/sm-118-2-101-115 %G en %F 10_4064_sm_118_2_101_115
Marius Junge. Comparing gaussian and Rademacher cotype for operators on the space of continuous functions. Studia Mathematica, Tome 118 (1996) no. 2, pp. 101-115. doi: 10.4064/sm-118-2-101-115
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