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OPTIMAL EXTENSIONS FOR POSITIVE ORDER CONTINUOUS OPERATORS ON BANACH FUNCTION SPACES

Published online by Cambridge University Press:  13 August 2013

O. DELGADO
O. DELGADO*
Affiliation:
Departamento de Matemática Aplicada I, E. T. S. de Ingeniería de Edificación, Universidad de Sevilla, Avenida Reina Mercedes, 4 A, 41012 Sevilla, Spain e-mail: olvido@us.es
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Abstract

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In this paper we give conditions under which a positive order continuous operator T defined on a Banach function space can be extended, preserving the order continuity in a certain optimal way. The optimal domain for T turns out to be a space of weakly integrable functions with respect to a vector measure (defined on a δ-ring) canonically associated to T. A similar result is obtained when T is σ-order continuous and we want to preserve the σ-order continuity. We apply these results to kernel operators.

Keywords

Primary 46G10Secondary 46E3046B42
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 3 , September 2014 , pp. 481 - 501
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

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