International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 63, Pages 3397-3407
doi:10.1155/S0161171204403585
Uniformly summing sets of operators on spaces of continuous
functions
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.
Abstract
Let X
and Y
be Banach spaces. A set ℳ
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
∑n‖Txn‖
is uniformly convergent in T∈ℳ. We study some general properties and
obtain a characterization of these sets when ℳ
is a set of operators defined on spaces of continuous functions.