Published January 8, 2021
| Version v1
Publication
Optimal domain of q-concave operators and vector measure representation of q-concave Banach lattices
Description
Given a Banach space valued q-concave linear operator T defined on a
σ-order continuous quasi-Banach function space, we provide a description of the
optimal domain of T preserving q-concavity, that is, the largest σ-order continuous
quasi-Banach function space to which T can be extended as a q-concave operator.
We show in this way the existence of maximal extensions for q-concave operators.
As an application, we show a representation theorem for q-concave Banach lattices
through spaces of integrable functions with respect to a vector measure. This
result culminates a series of representation theorems for Banach lattices using vector
measures that have been obtained in the last twenty years.
Abstract
Ministerio de Economía y Competitividad MTM2012-36732-C03-03Abstract
Junta de Andalucía FQM-262Abstract
Junta de Andalucía FQM-7276Additional details
Identifiers
- URL
- https://idus.us.es/handle//11441/103469
- URN
- urn:oai:idus.us.es:11441/103469