Optimal extensions for positive order continuous operators on Banach functions spaces

Description

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.

Abstract

Ministerio de Economía y Competitividad MTM2012-36732- C03-03

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Junta de Andalucía FQM-262

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Junta de Andalucía FQM-4643

Abstract

Junta de Andalucía FQM-7276

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