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Remarks on symmetric smooth norms

Published online by Cambridge University Press:  17 April 2009

P. H´Jek  and
V. Zizler
P. H´Jek
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
V. Zizler
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
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Abstract

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A characterisation is given of separable Banach spaces with symmetric Schauder bases which admit equivalent symmetric norms that are Gâteaux differentiable or uniformly rotund in every direction. Some applications to questions on distortion of norms on l∞ are discussed.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 2 , October 1995 , pp. 225 - 229
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Argyros, S. and Farmaki, V., ‘On the structure of weakly compact subsets of Hilbert spaces and applications to the geometry of Banach spaces’, Trans. Amer. Math. Soc. 289 (1985), 409–427.CrossRefGoogle Scholar
[2]Deville, R., Godefroy, G. and Zizler, V., Smoothness and renormings in Banach spaces, Monographs Surveys Pure Appl. Maths. 64 (Pitman, London, 1993).Google Scholar
[3]Hájek, P., ‘Polynomials and injections of Banach spaces into superreflexive spaces’, Arch. Math. 63 (1994), 39–44.CrossRefGoogle Scholar
[4]Hájek, P., ‘On convex functions in co(w1)1, Collect. Math. (to appear).Google Scholar
[5]Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces I. Sequence spaces (Springer-Verlag, Berlin, Heidelberg, New York, 1977).Google Scholar
[6]Troyanski, S., ‘On nonseparable Banach space with a symmetric basis’ Studio. Math. 53 (1975), 253–263.Google Scholar
[7]Troyanski, S., ‘Gâteaux differentiable norms in Lp’ Math. Ann. 287 (1990), 221–227.CrossRefGoogle Scholar
[8]Troyanski, S., ‘Equivalent norms in nonseparable Banach spaces with unconditional basis’, Teor. Funktsii˘ Funktsional Anal, i Prilozhen 6 (1968), 59–65.Google Scholar