Uniformly summing sets of operators on spaces of continuous functions

J. M. Delgado and Cándido Piñeiro

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-11

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 ( x n ) in X , the series ∑ n ‖ T x n ‖ 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.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:387279

DOI: 10.1155/S0161171204403585

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