A Criterion for Cv(X) to Be Quasinormable
Copyright policy )A Criterion for Cv(X) to Be Quasinormable
Let E be a locally convex vector space and \({\mathcal U}\) an arbitrary basis of zero neighbourhoods. Then E is called quasi-normable if for each \(U\in {\mathcal U}\) there is \(V\in {\mathcal U}\) such that \(V\subset U\) and for every \(\epsilon >0\), there is a bounded set \(B\subset E\) such that \(V\subset B+\epsilon U\). If X is a completely regular Hausdorff space, this paper study necessary and/or sufficient conditions for a ``weighted space'' on X and some of their subspaces to be quasi-normable.
- University of Paderborn Germany
- University of Liège Belgium
completely regular Hausdorff space, Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), weighted space, Topological linear spaces of continuous, differentiable or analytic functions, quasi-normable
completely regular Hausdorff space, Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), weighted space, Topological linear spaces of continuous, differentiable or analytic functions, quasi-normable
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).3 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!