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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Linear isometries between spaces of vector-valued Lipschitz functions


Authors: A. Jiménez-Vargas and Moisés Villegas-Vallecillos
Journal: Proc. Amer. Math. Soc. 137 (2009), 1381-1388
MSC (2000): Primary 46B04, 46E40; Secondary 46E15
Published electronically: October 20, 2008
MathSciNet review: 2465663
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Abstract: In this paper we state a Lipschitz version of a theorem due to Cambern concerning into linear isometries between spaces of vector-valued continuous functions and deduce a Lipschitz version of a celebrated theorem due to Jerison concerning onto linear isometries between such spaces.


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Additional Information

A. Jiménez-Vargas
Affiliation: Departamento de Álgebra y Análisis Matemático, Universidad de Almería, 04071, Almería, Spain
Email: ajimenez@ual.es

Moisés Villegas-Vallecillos
Affiliation: Departamento de Álgebra y Análisis Matemático, Universidad de Almería, 04071, Almería, Spain
Email: mvv042@alboran.ual.es

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09733-5
PII: S 0002-9939(08)09733-5
Keywords: Banach--Stone theorem, linear isometry, Lipschitz function
Received by editor(s): April 28, 2008
Published electronically: October 20, 2008
Additional Notes: The first author was partially supported by Junta de Andalucía grants FQM-1215 and FQM-1438, and by MEC grant MTM2006-4837
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2008 American Mathematical Society