A factorization constant for $l^n_p

N. Tenney Peck

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arXiv · math/9302213

A factorization constant for $l^n_p

N. Tenney Peck

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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.

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N. Tenney Peck. 1993-02-11. A factorization constant for $l^n_p. https://arxiv.org/abs/math/9302213

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