Holomorphic Functions on Strong Duals of Fréchet-Montel Spaces

Abstract

Publisher Summary This chapter investigates holomorphic functions defined on open subsets of duals of Frechet-Montel spaces, and shows that all the usual topologies coincide on such spaces and the pseudoconvex open subsets of duals of Frechet-Montel space are domains of existence of plurisubharmonic function. A locally convex infrabarralled space, in which every bounded set is relatively compact, is called a Montel space. A metrizable Montel space is a Frechet space and its strong dual is a Montel space and is called duals of Frechet-Montel spaces. Because Frechet-Montel spaces are separable and reflexive, it follows that the compact subsets are complete separable metrizable spaces. A topological space is a Souslin space, if it is the continuous image of a complete separable metrizable space. Countable inductive limits of Souslin spaces are also Souslin spaces. A topological space is a k-space if continuity on compact sets implies continuity. The equibounded sets of holomorphic function on arbitrary locally convex spaces are equicontinuous.