Montel and reflexive preduals of spaces of holomorphic functions on Fréchet spaces
Copyright policy )Montel and reflexive preduals of spaces of holomorphic functions on Fréchet spaces
Summary: For \(U\) open in a locally convex space \(E\) it is shown in [\textit{J. Mujica} and \textit{L. Nachbin}, J. Math. Pure Appl. 71, 543-560 (1992)] that there is a complete locally convex space \(G(U)\) such that \(G(U)_ i'= ({\mathcal H}(U), \tau_ \delta)\). Here, we assume \(U\) is balanced open in a Fréchet space and give necessary and sufficient conditions for \(G(U)\) to be Montel and reflexive. These results give an insight into the relationship between the \(\tau_ 0\) and \(\tau_ \omega\) topologies on \({\mathcal H}(U)\).
- University College Dublin Ireland
Reflexivity and semi-reflexivity, Spaces of differentiable or holomorphic functions on infinite-dimensional spaces, Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), Locally convex Fréchet spaces and (DF)-spaces, Fréchet space, Tensor products in functional analysis, Infinite-dimensional holomorphy
Reflexivity and semi-reflexivity, Spaces of differentiable or holomorphic functions on infinite-dimensional spaces, Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), Locally convex Fréchet spaces and (DF)-spaces, Fréchet space, Tensor products in functional analysis, Infinite-dimensional holomorphy
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).6 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!