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Eberlein compacts and spaces of continuous functions

Published online by Cambridge University Press:  24 October 2008

Richard J. Hunter  and
J. W. Lloyd
Richard J. Hunter
Affiliation:
University of Melbourne
J. W. Lloyd
Affiliation:
University of Melbourne
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Abstract

Let X be a Hausdorff topological space. We consider various locally convex spaces of continuous real valued functions on X and give necessary and sufficient conditions in order that (i) they contain an absolutely convex weakly compact total subset and (ii) they contain an absolutely convex total subset which is an Eberlein compact, when given the weak topology.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 85 , Issue 2 , March 1979 , pp. 305 - 313
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

REFERENCES

(1)Amir, D. and Lindenstrauss, J.The structure of weakly compact sets in Banach spaces. Ann. of Math. 88 (1968), 35–46.CrossRefGoogle Scholar
(2)Benyamini, Y., Rudin, M. E. and Wage, M.Continuous images of weakly compact subsets of Banach spaces. Pacific J. Math. 70 (1977), 309–324.CrossRefGoogle Scholar
(3)Dugundji, J.Topology (Boston, Allyn and Bacon, 1966).Google Scholar
(4)Grothendieck, A.Critères de compacité dans les espaces fonctionnels généraux. Amer. J. Math. 74 (1952), 168–186.CrossRefGoogle Scholar
(5)Hunter, R. J. and Lloyd, J.Weakly compactly generated locally convex spaces. Math. Proc. Cambridge Philos. Soc. 82 (1977), 85–97.CrossRefGoogle Scholar
(6)Köthe, G.Topological vector spaces, vol. 1 (Berlin, Heidelberg, New York, Springer–Verlag, 1969).Google Scholar
(7)Lindenstrauss, J.Weakly compact sets, their topological properties and the Banach spaces they generate. Symp. Inf. Dim. Topology, Ann. Math. Stud. 69 (1972), 235–273.Google Scholar
(8)Wilansky, A.Topology for analysis (Waltham, Mass., Ginn, 1970).Google Scholar