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Completion in the bidual

Published online by Cambridge University Press:  09 April 2009

R. Nielsen
R. Nielsen
Affiliation:
University of DelawareNewark, DelawareU.S.A.
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Let E, Ê, and E′ denote a locally convex linear Hausdorff space, completion of E and the dual of E, respectively. It has been observed that Ê is a subspace of E″ under certain conditions on E. It is the primary goal of this paper to give necessary and sufficient conditions for the Ê ⊂ E″ to be valid. Such conditions are found and are given Theorem 4. With a variation of the technique used, several equivalent characterizations of semi-reflexive spaces are given in Theorem 5. The nationa throughtout will follow that in [2].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 8 , Issue 2 , May 1968 , pp. 238 - 241
Copyright
Copyright © Australian Mathematical Society 1968

References

[1]Brace, J. W., ‘Convergence on filters and simple equivontinuity’, Ill. Journal Math., 9 (1965), 286–296.Google Scholar
[2]Horvath, J., Topological Vector Spaces (Addison-Wesley, 1966).Google Scholar
[3]Schaefer, H. H., Topological Vector Spaces (MacMillan, 1966, New York).Google Scholar