Abstract
This chapter discusses a duality theorem for nuclear function algebras. A is a nuclear function algebra if it is nuclear as a l.c.s. There are many examples naturally occurring in analysis. The chapter defines nuclear function algebras and discusses the examples and some basic properties for it. Nuclear function algebra on a non-finite space X is never a uniform Banach algebra. The chapter discusses the class of all nuclear function algebras to those that satisfy D. Vogt's condition. The space s of rapidly decreasing sequences plays a central part in the theory of nuclear (F)-spaces. The chapter discusses the duality theorem. The duality theorem is improved by a natural cohomological restriction. The chapter also characterizes the special analytic sets that are ordinary analytic sets in the sense of complex analysis of several variables.
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