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A base norm space whose cone is not 1-generating

Published online by Cambridge University Press:  18 May 2009

David Yost
David Yost
Affiliation:
Department of Pure Mathematics, La Trobe University, Bundoora, 3083 Victoria, Australia
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Let E be an ordered Banach space with closed positive cone C. A base for C is a convex subset K of C with the property that every non-zero element of C has a unique representation of the form λk with λ > 0 and k ∈ K. Let S be the absolutely convex hull of K. If the Minkowski functional of S coincides with the given norm on E, then E is called a base norm space. Then K is a closed face of the unit ball of E, and S contains the open unit ball of E. Base norm spaces were first defined by Ellis [5, p. 731], although the special case of dual Banach spaces had been studied earlier by Edwards [4].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 25 , Issue 1 , January 1984 , pp. 35 - 36
Copyright
Copyright © Glasgow Mathematical Journal Trust 1984

References

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