Comparing gaussian and Rademacher cotype for operators on the space of continous functions
Functional Analysis
2016-09-06 v1
Abstract
We will prove an abstract comparision principle which translates gaussian cotype in Rademacher cotype conditions and vice versa. More precisely, let and a linear, continous operator. T is of gaussian cotype q if and only if ( \summ_1^n (\frac{|| Tx_k||_F}{\sqrt{\log(k+1)}})^q )^{1/q} \, \le c || \summ_1^n \varepsilon_k x_k ||_{L_2(C(K))} , for all sequences with decreasing. T is of Rademacher cotype q if and only if (\summ_1^n (|| Tx_k||_F \,\sqrt{\log(k+1)})^q )^{1/q} \, \le c || \summ_1^n g_k x_k ||_{L_2(C(K))} , for all sequences with decreasing. Our methods allows a restriction to a fixed number of vectors and complements the corresponding results of Talagrand.
Keywords
Cite
@article{arxiv.math/9302206,
title = {Comparing gaussian and Rademacher cotype for operators on the space of continous functions},
author = {Marius Junge},
journal= {arXiv preprint arXiv:math/9302206},
year = {2016}
}