Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-06-05T20:27:44.550Z Has data issue: false hasContentIssue false
  • English
  • Français

Weak star separability

Published online by Cambridge University Press:  17 April 2009

E.N. Dancer  and
Brailey Sims
E.N. Dancer
Affiliation:
Department of Mathematics, University of New England, Armidale, New South Wales.
Brailey Sims
Affiliation:
Department of Mathematics, University of New England, Armidale, New South Wales.
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.

For a Banach space X, Susumu Okada raised the question of whether the unit hall of the dual space X* is weak* separable if X* is weak* separable. The problem occurred in the theory of manifolds modelled on locally convex spaces. We answer the question in the negative but show that it is true for particular types of spaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 20 , Issue 2 , April 1979 , pp. 253 - 257
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Day, Mahlon M., Normed linear spaces, 3rd ed. (Ergebnisse der Mathematik und ihrer Grenzgebiete, 21. Springer-Verlag, Berlin, Heidelberg, New York, 1973).Google Scholar
[2]Dunford, Nelson and Schwartz, Jacob T., Linear operators. Part I: General theory (Pure and Applied Mathematics, 7. Interscience, New York, London, 1958).Google Scholar
[3]Giles, J.R., Gregory, D.A., and Sims, Brailey, “Characterisation of normed linear spaces vith Mazur's intersection property”, Bull. Austral. Math. Soc. 18 (1978), 105–123.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]Namioka, I., “Separate continuity and joint continuity”, Pacific J. Math. 51 (1974, 515–531.Google Scholar
[6]Rudin, Walter, Functional analysis (McGraw-Hill, New York, St. Louis, San Francisco, Düsseldorf, Johannesburg, Kuala Lumpur, London, Mexico, Montreal, New Delhi, Panama, Rio de Janeiro, Singapore, Sydney, Toronto, 1973).Google Scholar
[7]Sims, Brailey, “Local agreement of the relative weak* and strong topologies on weak* compact sets and weak*-denting points”, submitted.Google Scholar
[8]Yost, David Thomas, “Spaces which admit convex norms” (MSc thesis, Australian National University, Canberra, 1977).Google Scholar