Corpus ID: 117055643

A factorization constant for $l^n_p

@article{Peck1993AFC,
  title={A factorization constant for \$l^n_p},
  author={N. Peck},
  journal={arXiv: Functional Analysis},
  year={1993}
}

N. Peck

Published 1993

Mathematics

arXiv: Functional Analysis

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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.