Resolutions of the identity in Fréchet spaces
✍ Scribed by W. J. Ricker
- Publisher
- SP Birkhäuser Verlag Basel
- Year
- 2001
- Tongue
- English
- Weight
- 667 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0378-620X
No coin nor oath required. For personal study only.
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## 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 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 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