Highly tempering infinite matrices II: From divergence to convergence via Toeplitz–Silverman matrices
It was recently proved [6] that for any Toeplitz{Silverman matrix A, there exists a dense linear subspace of the space of all sequences, all of whose nonzero elements are divergent yet whose images under A are convergent. In this paper, we improve and generalize this result by showing that, under su...
| Autores: | , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/7274 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/7274 |
| Access Level: | acceso abierto |
| Palavra-chave: | 512.64 517 Lineability Algebrability Latticeability Matrix summability Álgebra Análisis matemático 1201 Álgebra 1202 Análisis y Análisis Funcional |
| Resumo: | It was recently proved [6] that for any Toeplitz{Silverman matrix A, there exists a dense linear subspace of the space of all sequences, all of whose nonzero elements are divergent yet whose images under A are convergent. In this paper, we improve and generalize this result by showing that, under suitable assumptions on the matrix, there are a dense set, a large algebra and a large Banach lattice consisting (except for zero) of such sequences. We show further that one of our hypotheses on the matrix A cannot in general be omitted. The case in which the field of the entries of the matrix is ultrametric is also considered. |
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