Geodesic
A note on Köthe spaces
Glasgow mathematical journal, Tome 11 (1970) no. 2, pp. 152-155

Voir la notice de l'article provenant de la source Cambridge University Press

Let E be a locally compact space which can be expressed as the union of an increasing sequence of compact subsets Kn (n =1, 2, ...) and let μ be a positive Radon measure on E. Ω is the space of equivalence classes of locally integrable functions on E. We denote the equivalence class of a function f by and if is an equivalence class then f denotes any function belonging to f. Provided with the topology defined by the sequence of seminormsΩ is a Fréchet space. The dual of Ω is the space φ of equivalence classes of measurable, p.p. bounded functions vanishing outside a compact subset of E. For a subset Γ of Ω, the collection Λ of all ∊Ω, such that for each g∊Γ the product fg is integrable, is called a Köthe space and Γ is said to be the denning set of Λ. The Köthe space Λx which has Λ as a denning set is called the associated Kothe space of Λ. Λ and Λx are put into duality by the bilinear form 
Các, Nguyen Phuong. A note on Köthe spaces. Glasgow mathematical journal, Tome 11 (1970) no. 2, pp. 152-155. doi: 10.1017/S0017089500000999
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