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Mutual spaces and mutuality

Published online by Cambridge University Press:  24 October 2008

J. C. Amson
Affiliation:
The Mathematical Institute, St Andrews, Scotland

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
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

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