## Abstract Bierstedt and Bonet proved in 1988 that if a metrizable locally convex space __E__ satisfies the Heinrich's density condition, then every bounded set in the strong dual (__E__ ′, __β__ (__E__ ′, __E__)) of __E__ is metrizable; consequently __E__ is distinguished, i.e. (__E__ ′, __β__ (_
Basic Sequences in the Dual of a Fréchet Space
✍ Scribed by Manuel Valdivia
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 214 KB
- Volume
- 231
- Category
- Article
- ISSN
- 0025-584X
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📜 SIMILAR VOLUMES
## Preface. The class of quasi-normable locally convex spaces has been introduced by GROTHENDIECK [4]. Recently VALDIVIA [7] and BIERSTEDT, NEISE and SUMXERS [2], [3] independently gave a characterization of the quasirnormability of the FR~CRET-KOTHE spaces A(A) resp. P ( I , A ) in terms of the K
In this note we construct a non-separable Frtchet space E with the following properties: (i) No subspace of E is isomorphic to el. (ii) There is a linear form on E' which is bounded on bounded sets but is not continuous (i.e., the Mackey topology p(E, E ) is not bornological). This is a negative ans