Contemporary Mathematics
Volume 319, 2003
N on-archimedean Integral Operators on the space
of continuous functions
Jose Aguayo*
Departamento de Matematica,
Facultad de Ciencias Fisicas y Matematicas,
Universidad de Concepcion,
Casilla 160-C,
Miguel Nova
Departamento de Ciencias Basicas
Facultad de lngenieria
U niversidad Catolica de la Santisima Concepcion
Casilla 297
29 de octubre de 2002
In this paper we study the operators that we call integral operators.
We start it by giving the definition of integral operator and the definition
of integrable function with respect to this kind of operators. We prove a
necessary and sufficient condition to be a function integrable with respect
to a integral operator. We show that every continuous and bounded func-
tion is integrable with respect to any integral operator. We endow the
space all continuous functions with compact image with a locally convex
topology and we prove that a normed-valued linear operator defined on
this space is an integral operator if and only if it is continuous for this
locally convex topology.
1 Introduction and notation
Monna and Springer [4] started the study of non-archimedean integration. In
[5] , Van Rooij and Schikhof introduced some non-archimedean scalar measures
*Research supported by FONDECYT Grant No. 1990341, CONICYT-CHILE.
2000 Mathematics Subject Classification. Primary 28805, 46810, 47G10; Secondary
2003 American Mathematical Society
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