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Extending Edgar's ordering to locally convex spaces

Published online by Cambridge University Press:  18 May 2009

Neill Robertson
Neill Robertson
Affiliation:
Department of Mathematics, University of Cape Town, Rondebosch 7700, South Africa
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By the term “locally convex space”, we mean a locally convex Hausdorff topological vector space (see [17]). We shall denote the algebraic dual of a locally convex space E by E*, and its topological dual by E′. It is convenient to think of the elements of E as being linear functionals on E′, so that E can be identified with a subspace of E′*. The adjoint of a continuous linear map T:E→F will be denoted by T′:F′→E′. If 〈E, F〈 is a dual pair of vector spaces, then we shall denote the corresponding weak, strong and Mackey topologies on E by α(E, F), β(E, F) and μ(E, F) respectively.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 2 , May 1992 , pp. 175 - 188
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

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