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The uniform separation property and Banach-Stone theorems for lattice-valued Lipschitz functions


Authors: A. Jiménez-Vargas, A. Morales Campoy and Moisés Villegas-Vallecillos
Journal: Proc. Amer. Math. Soc. 137 (2009), 3769-3777
MSC (2000): Primary 46E40, 46E05
DOI: https://doi.org/10.1090/S0002-9939-09-09941-9
Published electronically: June 1, 2009
Erratum: Proc. Amer. Math. Soc. 138 (2010), 1535
MathSciNet review: 2529886
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Abstract | References | Similar Articles | Additional Information

Abstract: Using the uniform separation property of N. Weaver and the uniform joint property, we present in this paper a Lipschitz version of a Banach-Stone-type theorem for lattice-valued continuous functions obtained recently by J. X. Chen, Z. L. Chen and N.-C. Wong.


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Additional Information

A. Jiménez-Vargas
Affiliation: Departamento de Álgebra y Análisis Matemático, Universidad de Almería, 04120 Almería, Spain
Email: ajimenez@ual.es

A. Morales Campoy
Affiliation: Departamento de Álgebra y Análisis Matemático, Universidad de Almería, 04120 Almería, Spain
Email: amorales@ual.es

Moisés Villegas-Vallecillos
Affiliation: Departamento de Álgebra y Análisis Matemático, Universidad de Almería, 04120 Almería, Spain
Email: mvv042@alboran.ual.es

DOI: https://doi.org/10.1090/S0002-9939-09-09941-9
Keywords: Vector lattice isomorphism, lattice-valued Lipschitz function, Banach--Stone theorem, uniform separation property
Received by editor(s): February 12, 2009
Received by editor(s) in revised form: February 20, 2009
Published electronically: June 1, 2009
Additional Notes: This research was partially supported by Junta de Andalucía grants FQM-1438 and FQM-3737, and MCYT projects MTM2006-4837 and MTM2007-65959.
The third author was supported in part by Beca Plan Propio Universidad de Almería
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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