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

 

Universality of Asplund spaces


Authors: Petr Hájek, Gilles Lancien and Vicente Montesinos
Journal: Proc. Amer. Math. Soc. 135 (2007), 2031-2035
MSC (2000): Primary 46B30, 46B03
Published electronically: February 28, 2007
MathSciNet review: 2299476
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Abstract: Given any infinite cardinal $ \tau$, there exists no Banach space of density $ \tau$, which is Asplund or has the Point of Continuity Property and is universal for all reflexive spaces of density $ \tau$.


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Additional Information

Petr Hájek
Affiliation: Mathematical Institute, Czech Academy of Science, Žitná 25, 115 67 Praha 1, Czech Republic
Email: hajek@math.cas.cz

Gilles Lancien
Affiliation: Université de Franche Comté, Besancon, 16, Route de Gray, 25030 Besancon Cedex, France
Email: glancien@math.univ-fcomte.fr

Vicente Montesinos
Affiliation: Department of Applied Mathematics, Telecommunication Engineering Faculty, Polytechnic University of Valencia, 46071 Valencia, Spain
Email: vmontesi@mat.upv.es

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08780-1
PII: S 0002-9939(07)08780-1
Received by editor(s): January 17, 2006
Published electronically: February 28, 2007
Additional Notes: This work was supported by the following grants: Institutional Research Plan AV0Z10190503, A100190502, GA ČR 201/04/0090 and Project BMF2002-01423
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2007 American Mathematical Society