Very Strongly and Very Weakly Convergent Sequences in Locally Convex Spaces

We study very strong and very weak sequential convergence (notions which arise in infinite-dimensional holomorphy) and characterize, on the one hand, those locally convex spaces having a non-trivial, very strongly convergent sequence and, on the other, those spaces in which every sequence contains a...

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Bibliographic Details
Published in:Proceedings of the Royal Irish Academy. Section A: Mathematical and Physical Sciences 1984-01, Vol.84A (2), p.125-132
Main Author: Simões, Marilda A.
Format: Article
Language:English
Subjects:
Abstract spaces
Frechet topologies
Functional analysis
Linear transformations
Scalars
Topological spaces
Topological theorems
Topology
Online Access:Get full text
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Summary:We study very strong and very weak sequential convergence (notions which arise in infinite-dimensional holomorphy) and characterize, on the one hand, those locally convex spaces having a non-trivial, very strongly convergent sequence and, on the other, those spaces in which every sequence contains a very weakly convergent subsequence. Also some consequences of the characterizations obtained are discussed.
ISSN:0035-8975