Dual Pair Theory Applied to [Σ, a]-Domains

  • Charles E. Rickart
Part of the Universitext book series (UTX)


In this chapter we return to the study of general [Σ, a]-domains using the results for dual pairs <E, F> obtained in the preceding two chapters. It is desirable to review briefly the setting in which the theory of dual pairs may be brought to bear on the study of an arbitrary system [Σ, a]. In the first place, the algebra a, as a linear space with the compact-open topology, is a locally convex topological space (CLTS). Therefore its dual space a', consisting of all continuous linear functional,
together with a is a dual pair <a', a. Since point evaluations are continuous linear functionals on a and [Σ, a] is assumed to be a system the mapping
where <τ(σ), a> = a(σ) for all a ∈ a, is a homeomorphism of Σ into a', provided a' is given the σ(a', a-topology. Moreover we have the following proposition.


Holomorphic Function Point Evaluation Arbitrary Element Dual Pair Inductive Limit 
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Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • Charles E. Rickart
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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