Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-26T11:31:22.733Z Has data issue: false hasContentIssue false
  • English
  • Français

Mutual spaces and mutuality

Published online by Cambridge University Press:  24 October 2008

J. C. Amson
J. C. Amson
Affiliation:
The Mathematical Institute, St Andrews, Scotland
Get access Rights & Permissions [Opens in a new window]

Abstract

The theory of dual spaces and duality is extended from a pair of vector spaces in duality to a list of more than two vector spaces in mutuality. The notions of a canonical bilinear functional and of compatible topologies for a dual pair are extended to those of a canonical multilinear functional and of compatible topologies for a mutual list. Compatible topologies are characterized by means of an extended version of the Mackey–Arens Theorem. Directions for further work are noted.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 2 , March 1972 , pp. 203 - 210
Copyright
Copyright © Cambridge Philosophical Society 1972

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

(1)Treves, F.Topological vector spaces, distributions and kernels (Academic Press; New York, London, 1967).Google Scholar
(2)Wilansky, A.Functional analysis (Blaisdell; New York, London, 1964).Google Scholar