Hostname: page-component-6bf8c574d5-w79xw Total loading time: 0 Render date: 2025-02-22T21:02:45.289Z Has data issue: false hasContentIssue false
  • English
  • Français

Two counter-examples in nonseparable Banach spaces

Published online by Cambridge University Press:  17 April 2009

G.A. Alexandrov  and
M.I. Kadec
G.A. Alexandrov
Affiliation:
Department of Mathematics and Informatics, University of Sofia, 5 J. Bourchier Blvd, 1126 Sofia, Bulgaria
M.I. Kadec
Affiliation:
Pravda prosp. 5, Flat 26, 310022-Kharkov, Ukraine
Rights & Permissions [Opens in a new window]

Abstract

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.

It is shown that the well-known theorem of Kadec for the HГ renorming of separable Banach spaces, when Г is a norming subspace in the dual, cannot be extended to the class of nonseparable Banach spaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 1 , February 1994 , pp. 21 - 24
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Alexandrov, G.A., Locally uniformly convex equivalent norms in nonseparable Banach spaces, (in Russian), Ph.D. Dissertation: Kharkov, 1980.Google Scholar
[2]Alexandrov, G.A. and Kursten, K.-D., ‘Some nonseparable Banach spaces which admit equivalent locally uniformly convex norms’, in Russian, Izv. Vyssh. Ucheben. Zaved. Mat. 7 (1981), 10.Google Scholar
[3]Alexandrov, G.A., ‘Equivalent locally uniformly convex renorming of nonseparable Banach spaces’, in Russian, in Constructive function theory 81 (Varna 1981) (Bulgar. Acad. Sci., Sofia, 1983), pp. 9–13.Google Scholar
[4]Godun, B.V., ‘On the Markushevich bases’, in Russian, Dokl. Acad. Nauk SSSR 266 (1982), 11–14.Google Scholar
[5]Kadec, M.I., ‘On the connection between weak and strong convergence’, in Ukraninian, Dopovidi Acad. Nauk Ukrain. RSR 9 (1957), 949–952.Google Scholar
[6]Loomis, L.H., An introduction to abstract harmonic analysis (D. van Nostrand Co, Toronto, New York, London, 1953).Google Scholar
[7]Plicko, A.N., ‘On the projective resolution of identity, the Markushevich bases and the equivalent norms’, in Russian, Mat. Zametki 34 (1983), 719–726.Google Scholar