Dual Pair Theory Applied to [Σ, a]-Domains
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.
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© Springer-Verlag New York Inc. 1979