Negative results on the Nash-Moser theorem for Köthe sequence spaces and for spaces of ultradifferentiable functions
✍ Scribed by Markus Poppenberg
- Book ID
- 110558753
- Publisher
- Springer
- Year
- 1996
- Tongue
- English
- Weight
- 595 KB
- Volume
- 90
- Category
- Article
- ISSN
- 0025-2611
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## Abstract We study the asymptotic behavior of Maurey–Rosenthal type dominations for operators on Köthe function spaces which satisfy norm inequalities that define weak __q__ ‐concavity properties. In particular, we define and study two new classes of operators that we call __α__ ‐almost __q__ ‐co
In the paper, we shall prove that almost everywhere convergent bounded sequence in a Banach function space X is weakly convergent if and only if X and its dual space X\* have the order continuous norms. It follows that almost everywhere convergent bounded sequence in ¸N #¸N (1(p , p (R) is weakly co