Fréchet Schwartz spaces and approximation properties
✍ Scribed by Alfredo Peris
- Publisher
- Springer
- Year
- 1994
- Tongue
- English
- Weight
- 348 KB
- Volume
- 300
- Category
- Article
- ISSN
- 0025-5831
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
The reduction of the Ѩ-problem on a Frechet nuclear space to the study of the Ѩ-operator on a Hilbert space produces a global solution u when the second member w factors globally through this Hilbert space. Easy counterexamples show that this global factorization is not in general possible and hence
## Abstract An operator __T__ ∈ __L__(__E, F__) __factors over G__ if __T__ = __RS__ for some __S__ ∈ __L__(__E, G__) and __R__ ∈ __L__(__G, F__); the set of such operators is denoted by __L__^__G__^(__E, F__). A triple (__E, G, F__) satisfies __bounded factorization property__ (shortly, (__E, G, F
A smoothing property (S 0 ) t for Fre chet spaces is introduced generalizing the classical concept of smoothing operators which are important in the proof of Nash Moser inverse function theorems. For Fre chet Hilbert spaces property (0) in standard form in the sense of D. Vogt is shown to be suffici