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

 

On uniformly Gâteaux smooth norms and normal structure


Authors: Michal Johanis and Jan Rychtár
Journal: Proc. Amer. Math. Soc. 135 (2007), 1511-1514
MSC (2000): Primary 46B20
Published electronically: November 29, 2006
MathSciNet review: 2276661
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Abstract: It is shown that every separable Banach space admits an equivalent norm that is uniformly Gâteaux smooth and yet lacks asymptotic normal structure.


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Additional Information

Michal Johanis
Affiliation: Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
Email: johanis@karlin.mff.cuni.cz

Jan Rychtár
Affiliation: Department of Mathematical Sciences, University of North Carolina at Greensboro, Greensboro, North Carolina 27402
Email: rychtar@uncg.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08819-8
PII: S 0002-9939(06)08819-8
Keywords: Normal structure, asymptotic normal structure, uniformly G\^ateaux smooth norms
Received by editor(s): January 9, 2006
Published electronically: November 29, 2006
Additional Notes: The first author was supported by the research project MSM 0021620839 and by grant GAČR 201/05/P582
The second author was supported by the UNCG New Faculty Summer Excellence Grant 2005.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.



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