Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-15T10:44:01.887Z Has data issue: false hasContentIssue false
  • English
  • Français

An alternative proof of Diestel's theorem

Published online by Cambridge University Press:  18 May 2009

M. Ali Khan
M. Ali Khan
Affiliation:
The Johns Hopkins University, Baltimore Maryland 21218, U.S.A.
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 show that Diestel's theorem on weak compactness of subsets of L1,(μ, X) can be derived as a simple corollary of James's theorem. It is a pleasure to acknowledge several stimulating conserversations with Dave Emmons and the remarks of an anonymous referee. Errors are, of course, solely mine.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 25 , Issue 1 , January 1984 , pp. 45 - 46
Copyright
Copyright © Glasgow Mathematical Journal Trust 1984

References

REFERENCES

1.Brooks, J. K., Equicontinuous sets of measures and applications to Vitali's integral convergence theorem and control measures, Advances in Math. 10 (1973), 165–171.CrossRefGoogle Scholar
2.Davis, W. J., Figiel, T., Johnson, W. B. and Pelczynski, A., Factoring weakly compact operators, J. Functional Analysis 17 (1974), 311–327.CrossRefGoogle Scholar
3.Diestel, J., Remarks on weak compactness in L1,(μ, X), Glasgow Math. J. 18 (1977), 87–91.CrossRefGoogle Scholar
4.Diestel, J. and Uhl, J. J. Jr, Vector measures, American Mathematical Society (Providence, Rhode Island, 1977).CrossRefGoogle Scholar
5.James, R. C., Weakly compact sets, Trans. Amer. Math. Soc. 113 (1964), 129–140.CrossRefGoogle Scholar