A factorization constant for 𝑙ⁿ_{𝑝}, 0<𝑝<1

Peck, N. T.

doi:10.1090/S0002-9939-1994-1233980-2

A factorization constant for $l^ n_ p$, $0<p<1$
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Proc. Amer. Math. Soc. 121 (1994), 423-427 Request permission

Abstract:

We prove that if PT is a factorization of the identity operator on $\ell _p^n$ through $\ell _\infty ^k,0 < p$, then $\left \| P \right \| \left \| T \right \| \geq C{n^{1/p - 1/2}}{(\log n)^{ - 1/2}}$. This is a corollary of a more general result on factoring the identity operator on a quasi-normed space X through $\ell _\infty ^k$.

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