Computingp-summing norms with few vectors
نویسندگان
چکیده
منابع مشابه
Computing P–summing Norms with Few Vectors
It is shown that the p-summing norm of any operator with n-dimensional domain can be well-aproximated using only " few " vectors in the definition of the p-summing norm. Except for constants independent of n and log n factors, " few " means n if 1 < p < 2 and n p/2 if 2 < p < ∞.
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In this paper we improve a result of W. B. Johnson and G. Schechtman by proving that the p-summing norm of any operator with n-dimensional domain can be well-approximated using C(p)n logn(log logn)2 vectors if 1 < p < 2, and using C(p)np/2 logn if 2 < p <∞. 1. p-summing norms Throughout this paper we will follow notations of N. Tomczak-Jaegermann [To]. Definition 1.1. Let X and Y be Banach spac...
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CHRISTIAN HOUDRÉ , PHILIPPE MARCHAL and PATRICIA REYNAUD-BOURET School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA. E-mail: [email protected] CNRS and DMA, Ecole Normale Supérieure, 45 rue d’Ulm 75230 Paris Cedex 05, France. E-mail: [email protected] CNRS and DMA, Ecole Normale Supérieure, 45 rue d’Ulm 75230 Paris Cedex 05, France. E-mail: patricia.reynaud...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 1994
ISSN: 0021-2172,1565-8511
DOI: 10.1007/bf02772980