Representation Theorems for Operators on Free Banach Spaces of Countable Type


Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

This work will be centered in commutative Banach subalgebras of the algebra of bounded linear operators defined on free Banach spaces of countable type. The main goal of this work will be to formulate a representation theorem for these operators through integrals defined by spectral measures type. In order to get this objective, we will show that, under special conditions, each one of these algebras is isometrically isomorphic to some space of continuous functions defined over a compact set. Then, we will identify such compact sets developing the Gelfand space theory in the non-Archimedean setting. This fact will allow us to define a measure which is known as spectral measure. As a second goal, we will formulate a matrix representation theorem for this class of operators in which the entries of the matrices will be integrals coming from scalar measures.

About the authors

J. Aguayo

Departamento de Matemática, Facultad de Ciencias Físicas y Matemáticas

Author for correspondence.
Email: jaguayo@udec.cl
Chile, Casilla 160-C, Concepción

M. Nova

Departamento de Matemática y Física Aplicadas, Facultad de Ingeniería

Email: jaguayo@udec.cl
Chile, Casilla 297, Concepción

J. Ojeda

Departamento de Matemática, Facultad de Ciencias Físicas y Matemáticas

Email: jaguayo@udec.cl
Chile, Casilla 160-C, Concepción

Supplementary files

Supplementary Files
Action
1. JATS XML

Copyright (c) 2019 Pleiades Publishing, Ltd.