Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-15T15:47:24.717Z Has data issue: false hasContentIssue false
  • English
  • Français

Some remarks on regular Banach spaces

Published online by Cambridge University Press:  18 May 2009

Denny H. Leung
Denny H. Leung
Affiliation:
Department of Mathematics, National University of Singapore, Singapore0511, E-mail address: matlhh@leonis.nus.sg
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.

A Banach space E is said to be regular if every bounded linear operator from E into E′ is weakly compact. This property was studied in [7, 9] under the name Property (w). In [7], using James type spaces as constructed in [4], examples were given of regular Banach spaces which fail to have weakly sequentially complete duals, answering a question raised in [9]. In this paper, we present some more results concerning the regularity of James type spaces.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 2 , May 1996 , pp. 243 - 248
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

References

REFERENCES

1.Andrew, Alfred, James' quasi-reflexive space is not isomorphic to any subspace of its dual, Israel J. Math. 38 (1981), 276–282.CrossRefGoogle Scholar
2.Aron, R. M., Cole, B. J., and Gamelin, T. W., Spectra of algebras of analytic functions on a Banach space, J. reine angew. Math. 415 (1991), 51–93.Google Scholar
3.Aron, R. M., Galindo, P., Garcia, D., and Maestre, M., Regularity and algebras of analytic functions in infinite domains, preprint.Google Scholar
4.Bellenot, Steven F., Haydon, Richard, and Odell, Edward, Quasi-reflexive and tree spaces constructed in the spirit of R. C. James, Contemporary Math. 85 (1989), 19–43.CrossRefGoogle Scholar
5.James, Robert C., A non-reflexive Banach space isometric with its second conjugate space, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 174–177.CrossRefGoogle ScholarPubMed
6.James, Robert C., Banach spaces quasi-reflexive of order one, Studia Math. 60 (1977), 157–177.CrossRefGoogle Scholar
7.Leung, Denny H., Banach spaces with property (w), Glasgow Math. J. 35 (1993), 207–217.CrossRefGoogle Scholar
8.Lindenstrauss, Joram and Tzafriri, Lior, Classical Banach Spaces I, Sequence Spaces, (Springer-Verlag, 1977).Google Scholar
9.Saab, E. and Saab, P., Extensions of some classes of operators and applications, Rocky Mountain J. Math. 23, no. 1 (1993), 319–337.CrossRefGoogle Scholar