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On Weak* Kadec–Klee Norms

Published online by Cambridge University Press:  20 November 2018

Jan Rychtář  and
Jiří Spurný
Jan Rychtář
Affiliation:
Department of Mathematical and Statistical Sciences, University of North Carolina at Greensboro, Greensboro, NC 27402, U.S.A. e-mail: rychtar@uncg.edu
Jiří Spurný
Affiliation:
Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic e-mail: spurny@karlin.mff.cuni.cz
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Abstract

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We present partial positive results supporting a conjecture that admitting an equivalent Lipschitz (or uniformly) weak* Kadec–Klee norm is a three space property.

Keywords

46B0346B20weak* Kadec–Klee normsthree-space problem
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 50 , Issue 4 , 01 December 2007 , pp. 610 - 618
Copyright
Copyright © Canadian Mathematical Society 2007

References

[1] Deville, R., Godefroy, G. and Zizler, V., Smoothness and Renormings of Banach Spaces. Pitman Monographs 64, New York, 1993.Google Scholar
[2] Godefroy, G., Kalton, N. and Lancien, G., Subspaces of c 0(ℕ) and Lipschitz isomorphisms. Geom. Funct. Anal. 10(2000), no. 4, 798–820.Google Scholar
[3] Fabian, M., Habala, P., Hájek, P., Montesinos, V., Pelant, J. and and Zizler, V., Functional Analysis and Infinite-Dimensional Geometry. Springer-Verlag, New York, 2001.Google Scholar
[4] Johnson, W. B. and Lindenstrauss, J., Some remarks on weakly compactly generated Banach spaces. Israel J. Math. 17(1974), 219–230.Google Scholar
[5] Lancien, G., On the Szlenk Index and the weak*-dentability index. Quart. J. Math. Oxford 47(1996), 59–71.Google Scholar
[6] Lancien, G., On uniformly convex and uniformly Kadec-Klee renormings. Serdica Math. J. 21(1995), 1–18.Google Scholar
[7] Rychtář, J., Renormings of C(K) spaces. Proc. Amer. Math. Soc. 131(2003), 2063–2070.Google Scholar