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International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 5, Pages 307-312
http://dx.doi.org/10.1155/S0161171202007688

A note on uniformly dominated sets of summing operators

Departamento de Matemáticas, Escuela Politécnica Superior, Universidad de Huelva, La Rábida 21819, Huelva, Spain

Received 26 May 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let Y be a Banach space that has no finite cotype and p a real number satisfying 1p<. We prove that a set Πp(X,Y) is uniformly dominated if and only if there exists a constant C>0 such that, for every finite set {(xi,Ti):i=1,,n}X×, there is an operator TΠp(X,Y) satisfying πp(T)C and TixiTxi for i=1,,n.