## 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__ (_
A characterization of totally reflexive Fréchet spaces
✍ Scribed by M. Valdivia
- Publisher
- Springer-Verlag
- Year
- 1989
- Tongue
- French
- Weight
- 704 KB
- Volume
- 200
- Category
- Article
- ISSN
- 0025-5874
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📜 SIMILAR VOLUMES
## Abstract A Fréchet space __E__ is quasi‐reflexive if, either dim(__E__″/__E__) < ∞, or __E__″[__β__(__E__″,__E__′)]/__E__ is isomorphic to __ω__. A Fréchet space __E__ is totally quasi‐reflexive if every separated quotient is quasi‐reflexive. In this paper we show, using Schauder bases, that __E
## 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