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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
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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

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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