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On uniformly Gâteaux smooth norms and normal structure
Author(s):
Michal
Johanis;
Jan
Rychtár
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1511-1514.
MSC (2000):
Primary 46B20
Posted:
November 29, 2006
MathSciNet review:
2276661
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Additional information
Abstract:
It is shown that every separable Banach space admits an equivalent norm that is uniformly Gâteaux smooth and yet lacks asymptotic normal structure.
References:
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- [BS]
- J.B. Baillon and R. Schöneberg, Asymptotic normal structure and fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 81 (1981), no. 2, 257-264. MR 0593469 (82c:47068)
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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:
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
Posted:
November 29, 2006
Additional Notes:
The first author was supported by the research project MSM 0021620839 and by grant GACR 201/05/P582
The second author was supported by the UNCG New Faculty Summer Excellence Grant 2005.
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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