A factorization constant for $l^n_p
Functional Analysis
2016-09-06 v1
Abstract
We prove that if PT is a factorization of the identity operator on \ell_p^n through \ell_{\infty}^k, then ||P|| ||T|| \geq Cn^{1/p-1/2}(log n)^{-1/2}. This is a corollary of a more general result on factoring the identity operator on a quasi-normed space through \ell_{\infty}^k.
Cite
@article{arxiv.math/9302213,
title = {A factorization constant for $l^n_p},
author = {N. Tenney Peck},
journal= {arXiv preprint arXiv:math/9302213},
year = {2016}
}