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XI.—On Unconditional Convergence in Topological Vector Spaces

Published online by Cambridge University Press:  14 February 2012

A. P. Robertson
A. P. Robertson
Affiliation:
Department of Mathematics, University of Keele.
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Synopsis

For a series of elements of a topological vector space, necessary and sufficient conditions are found, in terms of the set of finite partial sums, for unconditional convergence and for the corresponding Cauchy condition. The extent to which these results remain valid for topological groups is investigated. A new and direct proof, for locally convex spaces, is given of the theorem of Orlicz.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 68 , Issue 2 , 1969 , pp. 145 - 157
Copyright
Copyright © Royal Society of Edinburgh 1969

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References

References to Literature

Grothendieck, A., 1953. “Sur les applications linéaires faiblement compactes d'espaces du type C(K)”, Can.J. Math., 5, 129–173.CrossRefGoogle Scholar
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Orlicz, W., 1929. “Beiträge zur Theorie der Orthogonalentwicklungen II”, Studia Math., 1, 241–255.Google Scholar
Pettis, B. J., 1938. “On integration in vector spaces”, Trans. Am. Math. Soc., 44, 277–304.CrossRefGoogle Scholar