A problem on the structure of Fréchet spaces
✍ Scribed by José Bonet
- Book ID
- 119937736
- Publisher
- Springer Milan
- Year
- 2010
- Tongue
- English
- Weight
- 156 KB
- Volume
- 104
- Category
- Article
- ISSN
- 1578-7303
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract We characterize tame pairs (__X__, __Y__) of Fréchet spaces where either __X__ or __Y__ is a power series space. For power series spaces of finite type, we get the well‐known conditions of (__DN__)‐(Ω) type. On the other hand, for power series spaces of infinite type, surprisingly, tame
## 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__ (_
## Abstract It is proved when a non‐Archimedean Fréchet space __E__ of countable type has a quotient isomorphic to 𝕂^ℕ^, __c__^ℕ^~0~ or __c__~0~ × 𝕂^ℕ^. It is also shown when __E__ has a non‐normable quotient with a continuous norm. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)