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On the Radon-Nikodym property in function spaces


Authors: Guillermo P. Curbera and Werner J. Ricker
Journal: Proc. Amer. Math. Soc. 145 (2017), 617-626
MSC (2010): Primary 46G05, 46E30; Secondary 28B05
DOI: https://doi.org/10.1090/proc/13414
Published electronically: October 13, 2016
MathSciNet review: 3577865
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Abstract: We exhibit a large class of Banach function spaces which fail to have the Radon-Nikodym property.


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Guillermo P. Curbera
Affiliation: Facultad de Matemáticas & IMUS, Universidad de Sevilla, Aptdo. 1160, Sevilla 41080, Spain
Email: curbera@us.es

Werner J. Ricker
Affiliation: Math.–Geogr. Fakultät, Katholische Universität Eichstätt–Ingolstadt, D–85072 Eichstätt, Germany
Email: werner.ricker@ku.de

DOI: https://doi.org/10.1090/proc/13414
Keywords: Radon-Nikodym property, Banach function space, vector measure, kernel operator
Received by editor(s): January 11, 2016
Published electronically: October 13, 2016
Additional Notes: The first author acknowledges the support of the “International Visiting Professor Program 2015” from the Ministry of Education, Science and Art, Bavaria (Germany), and of MTM2012-36732-C03-03, MINECO (Spain).
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2016 American Mathematical Society