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In what spaces is every closed normal cone regular?

Published online by Cambridge University Press:  20 January 2009

C. W. McArthur
C. W. McArthur
Affiliation:
The Florida State University, Tallahassee, Florida
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It is known (13, p. 92) that each closed normal cone in a weakly sequentially complete locally convex space is regular and fully regular. Part of the main theorem of this paper shows that a certain amount of weak sequential completeness is necessary in order that each closed normal cone be regular. Specifically, it is shown that each closed normal cone in a Fréchet space is regular if and only if each closed subspace with an unconditional basis is weakly sequentially complete. If E is a strongly separable conjugate of a Banach space it is shown that each closed normal cone in E is fully regular. If E is a Banach space with an unconditional basis it is shown that each closed normal cone in E is fully regular if and only if E is the conjugate of a Banach space.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 17 , Issue 2 , December 1970 , pp. 121 - 125
Copyright
Copyright © Edinburgh Mathematical Society 1970

References

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