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Renorming James tree space
Author(s):
Petr
Hájek;
Jan
Rychtár
Journal:
Trans. Amer. Math. Soc.
357
(2005),
3775-3788.
MSC (2000):
Primary 46B03
Posted:
March 31, 2005
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Abstract:
We show that the James tree space  can be renormed to be Lipschitz separated. This negatively answers the question of J. Borwein, J. Giles and J. Vanderwerff as to whether every Lipschitz separated Banach space is an Asplund space.
References:
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Additional Information:
Petr
Hájek
Affiliation:
Mathematical Institute, AV CR, Zitná
25,
115 67 Praha 1, Czech Republic
Email:
hajek@math.cas.cz
Jan
Rychtár
Affiliation:
Department of Mathematical and Statistical Sciences,
University of Alberta, Edmonton, Alberta, Canada
T6G 2G1
Address at time of publication:
Department of Mathematical Sciences, University of North Carolina, Greensboro, North Carolina 27402
Email:
jrychtar@math.ualberta.ca
DOI:
10.1090/S0002-9947-05-03691-3
PII:
S 0002-9947(05)03691-3
Keywords:
Rotund norms,
James tree space,
Lipschitz separated Banach spaces
Received by editor(s):
October 3, 2003
Received by editor(s) in revised form:
March 25, 2004
Posted:
March 31, 2005
Additional Notes:
The first author was supported by GACR 201/01/1198 and A 101 92 05. The second author was supported by GACR 201/04/0090, GAUK 277/2001 and NSERC 7926.
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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