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Transactions of the American Mathematical Society

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Renorming James tree space

Authors: Petr Hájek and Jan Rychtár
Journal: Trans. Amer. Math. Soc. 357 (2005), 3775-3788
MSC (2000): Primary 46B03
Published electronically: March 31, 2005
MathSciNet review: 2146649
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Abstract: We show that the James tree space $JT$ 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.

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  • 1. J. BORWEIN, J. GILES AND J. VANDERWERFF: Rotund norms, Clarke subdifferentials and extensions of Lipschitz functions, Nonlinear Analysis 48, 2002, 287-301. MR 1870757 (2002h:49024)
  • 2. R. DEVILLE, G. GODEFROY AND V. ZIZLER: Smoothness and renormings in Banach spaces, Pitman Monographs and Surveys in Pure and Applied Mathematics 64, Longman, 1993.MR 1211634 (94d:46012)
  • 3. P. ENFLO: Banach spaces which can be given an equivalent uniformly convex norm, Israel J. Math. 13, 1972, 281-288. MR 0336297 (49:1073)
  • 4. M. FABIAN, P. HABALA, P. H´AJEK, V. MONTESINOS, J. PELANT AND V. ZIZLER: Functional analysis and infinite dimensional geometry, Canadian Math. Soc. Books (Springer-Verlag), 2001. MR 1831176 (2002f:46001)
  • 5. P. H´AJEK: Dual reormings of Banach spaces, Comment. Math. Univ. Carolinae 37, 1996, 241-554.MR 1398999 (97h:46013)
  • 6. J. LINDENSTRAUSS AND C. STEGALL: Examples of separable spaces which do not contain $\ell_1$ and whose duals are nonseparable, Studia Math. 54, 1975, 81-105.MR 0390720 (52:11543)
  • 7. E. ODELL AND T. SCHLUMPRECHT: On asymptotic properties of Banach spaces under renormings, J. Amer. Math. Soc. 11, 1998, 175-188.MR 1469118 (98h:46006)

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Additional Information

Petr Hájek
Affiliation: Mathematical Institute, AV ČR, Žitná 25, 115 67 Praha 1, Czech Republic

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

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
Published electronically: March 31, 2005
Additional Notes: The first author was supported by GAČR 201/01/1198 and A 101 92 05. The second author was supported by GAČR 201/04/0090, GAUK 277/2001 and NSERC 7926.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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