Comparing gaussian and Rademacher cotype for operators on the space of continuous functions
Studia Mathematica, Tome 118 (1996) no. 2, pp. 101-115
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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},
publisher = {mathdoc},
volume = {118},
number = {2},
year = {1996},
doi = {10.4064/sm-118-2-101-115},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-118-2-101-115/}
}
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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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