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,

Concepcion-Chile

Miguel Nova

Departamento de Ciencias Basicas

Facultad de lngenieria

U niversidad Catolica de la Santisima Concepcion

Casilla 297

Concepcion-Chile

29 de octubre de 2002

Resumen

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.

0

2000 Mathematics Subject Classification. Primary 28805, 46810, 47G10; Secondary

47G12.

©

2003 American Mathematical Society

1

http://dx.doi.org/10.1090/conm/319/05561