International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 63, Pages 3397-3407

Uniformly summing sets of operators on spaces of continuous functions

J. M. Delgado and Cándido Piñeiro

Departamento de Matemáticas, Facultad de Ciencias Experimentales, Campus Universitario del Carmen, Avda. de las Fuerzas Armadas, Huelva 21071 , Spain

Received 30 March 2004

Copyright © 2004 J. M. Delgado and Cándido Piñeiro. 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.


Let X and Y be Banach spaces. A set of 1-summing operators from X into Y is said to be uniformly summing if the following holds: given a weakly 1-summing sequence (xn) in X, the series nTxn is uniformly convergent in T. We study some general properties and obtain a characterization of these sets when is a set of operators defined on spaces of continuous functions.