Properties \((\text{DN}_{(\phi,\psi)})\) and \(\Omega_{(\phi,\psi)}\) for Fréchet spaces (Q1924924)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Properties \((\text{DN}_{(\phi,\psi)})\) and \(\Omega_{(\phi,\psi)}\) for Fréchet spaces |
scientific article; zbMATH DE number 938551
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Properties \((\text{DN}_{(\phi,\psi)})\) and \(\Omega_{(\phi,\psi)}\) for Fréchet spaces |
scientific article; zbMATH DE number 938551 |
Statements
Properties \((\text{DN}_{(\phi,\psi)})\) and \(\Omega_{(\phi,\psi)}\) for Fréchet spaces (English)
0 references
10 November 1996
0 references
The quantitative variants \((\text{DN}_{(\phi,\psi)})\) and \((\Omega_{(\phi,\psi)})\) of properties (DN) and \((\Omega)\) are introduced for Fréchet spaces. A Köthe sequence space is shown to have property \((\text{DN}_{(\phi,\psi)})\) (resp. \((\Omega_{(\phi,\psi)})\)) iff it is \((\phi,\psi)\)-tamely isomorphic to some Köthe space with a logarithmically convex (resp. concave) system of seminorms; here \((\phi,\psi)\) are a measure for the continuity estimates. As an application, quantitative variants of the well-known (DN)-\((\Omega)\) splitting theorem of D. Vogt are obtained.
0 references
topological invariants
0 references
tamely isomorphic
0 references
Fréchet spaces
0 references
Köthe sequence space
0 references
splitting theorem
0 references
