Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-06T09:49:02.440Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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
McArthur, C. W., 1967. “On a theorem of Orlicz and Pettis”, Pacif.J. Math., 22, 297–302.Google Scholar
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