Article
Köthe echelon spaces à la Dieudonné
Author/s | Florencio Lora, Miguel
Paúl Escolano, Pedro José ![]() ![]() ![]() ![]() ![]() ![]() ![]() Sáez Agulló, Carmen ![]() ![]() ![]() ![]() ![]() |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Publication Date | 1994 |
Deposit Date | 2021-08-11 |
Published in |
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Abstract | Let (gn) be a sequence of locally integrable functions defined on a Radon measure space. The echelon space associated to (gn) was defined by J. Dieudonné as the Köthe-dual of (gn), i.e. the space Λ of all locally integrable ... Let (gn) be a sequence of locally integrable functions defined on a Radon measure space. The echelon space associated to (gn) was defined by J. Dieudonné as the Köthe-dual of (gn), i.e. the space Λ of all locally integrable functions f such that all the integrals ∫ |f·gn| are finite. Denote by Λx the Köthe-dual of Λ. We prove that Λ(β(Λ,Λx)) is a Fréchet space with dual Λx. This result gives its correct sense to a wrong affirmation of J. Dieudonné and validates those instances where it has been used. As a tool to prove this result, we study the problem of when the strong dual of a perfect space coincides with its Köthe-dual and give some necessary and sufficient conditions. |
Citation | Florencio Lora, M., Paúl Escolano, P.J. y Sáez Agulló, C. (1994). Köthe echelon spaces à la Dieudonné. Indagationes Mathematicae, 5 (1), 51-60. |
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