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Countable-Codimensional Subspaces of c0-Barrelled Spaces

✍ Scribed by J. M. Garcia-Lafuente

Publisher
John Wiley and Sons
Year
1987
Tongue
English
Weight
327 KB
Volume
130
Category
Article
ISSN
0025-584X

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✦ Synopsis

A HAUSDORFF locally convex space is said to be c,-barrelled (respectively cu-barrelled) if each sequence in the dual space t h a t converges weakly to 0 (res!,r:ctively t h a t is weakly ?.~oundecl), is equicontinuous. It is proved that if a c,,-barrelled space E has dual E' weakly sequentially complete, then every subsi'ace of countable codimensjon of E is c,-barrcllecl. %Ire prove that the hypothesis on E' cannot be dropped and we supply a n esniiiple of a complete c,,-hnrrellecl space with dual wealily sequentially coin1)lete that is not co-barrelled.

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