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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

Gilles Lancien
Affiliation: Université de Franche Comté, Besancon, 16, Route de Gray, 25030 Besancon Cedex, France

Vicente Montesinos
Affiliation: Department of Applied Mathematics, Telecommunication Engineering Faculty, Polytechnic University of Valencia, 46071 Valencia, Spain

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

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