In this paper we investigate a property named GL(p,q) which is closely
related to the Gordon-Lewis property. Our results on GL(p,q) are then used to
estimate volume ratios relative to $\ell_p$, $1<p \le\infty$, of unconditional
direct sums of Banach spaces

Gordon, Yehoram

Junge, Marius

Nielsen, Niels Jorgen

English

arXiv

In this paper we investigate a property named GL(p; q) which is closely related to the Gordon-Lewis property. Our results on GL(p; q) are then used to estimate volume ratios relative to ` p , 1 ! p  1, of unconditional direct sums of Banach spaces. Introduction  In this paper we investigate a property named GL(p; q), 1  p  1, 1  q  1, closely related to the Gordon-Lewis property GL, and the behavior of p-summing norms of operators defined on direct sums of Banach spaces in the sense of an unconditional basis. These results are then used to estimate the volume ratios vr(X; ` p ), 1 ! p  1, where X is a finite direct sum of finite dimensional spaces. A Banach space is said to have GL(p; q), 1  p  1, 1  q  1, if there is a constant C so that i q (T )  Cß p (T    ) for every finite rank operator T from an arbitrary Banach space to X . Here  ß p denotes the p-summing norm and i q the q-integral norm. This property was also considered by Reisner [27], note however the slight difference in th..

Y. Gordon

M. Junge

N. J. Nielsen

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The Relations between Volume Ratios and New Concepts of GL Constants

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.7584

The relations between volume ratios and new concepts of gl constants

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