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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A factorization constant for $ l\sp n\sb p$, $ 0<p<1$


Author: N. T. Peck
Journal: Proc. Amer. Math. Soc. 121 (1994), 423-427
MSC: Primary 46A16; Secondary 46B07
MathSciNet review: 1233980
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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,0 < p$, then $ \left\Vert P \right\Vert \left\Vert T \right\Vert \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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DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1233980-2
PII: S 0002-9939(1994)1233980-2
Keywords: Factorization of the identity, $ \ell _p^n,0 < p < 1,\ell _\infty ^n$, factorization constant, Rademacher functions, Hahn-Banach extension
Article copyright: © Copyright 1994 American Mathematical Society