Hostname: page-component-84b7d79bbc-lrf7s Total loading time: 0 Render date: 2024-07-30T11:23:36.814Z Has data issue: false hasContentIssue false
  • English
  • Français

On biorthogonal systems and Maxur's intersection property

Published online by Cambridge University Press:  17 April 2009

Jan Rychtář
Jan Rychtář
Affiliation:
Department of Mathematical and Statistical Science, University of Alberta, Edmonton, Alberta T6G 2G1Canada, e-mail: jrychtar@math.ualberta.ca
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give a characterisation of Banach spaces X containing a subspace with a shrinking Markushevich basis {xγ, fγ}γ∈Γ. This gives a sufficient condition for X to have a renorming with Mazur's intersection property.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 1 , February 2004 , pp. 107 - 111
Copyright
Copyright © Australian Mathematical Society 2004

References

[1] Deville, R., Godefroy, G. and Zizler, V., Smoothness and renormings in Banach spaces, Pitmen Monographs and Surveys in Pure and Applied Mathematics 64 (Longman scientific and Technical, Harlow, 1993).Google Scholar
[2] Fabian, M., Habala, P., Hájek, P., Montesinos, V., Pelant, J. and Zizler, V., Functional analysis and infinite dimensional geometry, CMS Books in Mathematics 8 (Springer-Verlag, New York, 2001).CrossRefGoogle Scholar
[3] Giles, J.R., Gregory, D.A., and Sims, B., ‘Characterization of normed linear spaces with Mazur's intersection property’, Bull. Austral. Math. Soc. 18 1978, 471–476.CrossRefGoogle Scholar
[4] Godefroy, G., ‘Asplund spaces and decomposable nonseparable Banach spaces’, Rocky Mountain J. Math. 25 1995, 1013–1024.CrossRefGoogle Scholar
[5] Holický, P., Šmidek, M., Zajíček, L., ‘Convex functions with non-Borel set of Gâteaux differentiability points’, Comment. Math. Univ. Carolin. 39 1998, 469–482.Google Scholar
[6] Sevilla, M. Jiménez and Moreno, J. P., ‘Renorming Banach spaces with the Mazur intersection property’, J. Funct. Anal. 144 1997, 486–504.CrossRefGoogle Scholar
[7] Lindernstrauss, J. and Tzafriri, L., Classical Banach spaces I (Springer-Verlag, Berlin, Heidelberg, New York 1977).CrossRefGoogle Scholar
[8] Negrepontis, S., ‘Banach spaces and topology’, in Handbook of Set Theoretic Topology, (Kunen, K. and Vaughan, J.E., Editors) (North-Holland, Amsterdam, 1984), pp. 1045–1142.CrossRefGoogle Scholar
[9] Zizler, V., ‘Nonseparable Banach spaces’, in Handbook of the geometry of Banach spaces, Vol. II, (Johnson, W.B. and Lindenstrauss, J., Editors). (Elsevier, Amsterdam, 2003).Google Scholar