Mixed vector space topologies

Queiroz, Maria Lúcia B. de

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Holomorphic functions on locally convex topological vector spaces. I. Locally convex topologies on $ℋ (U)$

Sean Dineen (1973)

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This article is devoted to a study of locally convex topologies on $H (U)$ (where $U$ is an open subset of the locally convex topological vector space $E$ and $H (U)$ is the set of all complex valued holomorphic functions on $E$ ). We discuss the following topologies on $H (U)$ : (a) the compact open topology $I_{0}$ , (b) the bornological topology associated with $I_{0}$ , (c) the ported topology of Nachbin $I_{ω}$ , (d) the bornological topology associated with $I_{ω}$ ; and ...

Quasinormability of some spaces of holomorphic mappings.

José M. Isidro (1990)

Revista Matemática de la Universidad Complutense de Madrid

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A class of locally convex vector spaces with a special Schauder decomposition is considered. It is proved that the elements of this class, which includes some spaces naturally appearing in infinite dimensional holomorphy, are quasinormable though in general they are neither metrizable nor Schwartz spaces.