Artículo
Barrelledness of Spaces with Toeplitz Decompositions
Autor/es | Paúl Escolano, Pedro José
Sáez Agulló, Carmen Virués Gavira, Juan Manuel |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Fecha de publicación | 1999 |
Fecha de depósito | 2021-09-10 |
Publicado en |
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Resumen | A Toeplitz decomposition of a locally convex space E into subspaces (Ek) with projections (Pk) is a decomposition of every x ∈ E as x = ∑kPkx, where ordinary summability has been replaced by summability with respect to an ... A Toeplitz decomposition of a locally convex space E into subspaces (Ek) with projections (Pk) is a decomposition of every x ∈ E as x = ∑kPkx, where ordinary summability has been replaced by summability with respect to an infinite and lower triangular regular matrix. We extend to the setting of Toeplitz decompositions a couple of results about barrelledness of Schauder decompositions. The first result, given for Schauder decompositions by Noll and Stadler, links the barrelledness of a normed space E to the barrelledness of the pieces Ek via the fact that E′ is big enough so as to coincide with its summability dual. Our second theorem, given for Schauder decompositions by Dı́az and Miñarro, links the quasibarrelledness of an ℵ0-quasibarrelled (in particular, (DF)) space E to the quasibarrelledness of the pieces Ek via the fact that the decomposition is simple. |
Cita | Paúl Escolano, P.J., Sáez Agulló, C. y Virués Gavira, J.M. (1999). Barrelledness of Spaces with Toeplitz Decompositions. Journal of Mathematical Analysis and Applications, 240 (2), 468-480. |
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