RT Journal Article
T1 Highly tempering infinite matrices II: From divergence to convergence via Toeplitz–Silverman matrices
A1 Bernal González, L.
A1 Fernández Sánchez, Juan
A1 Seoane Sepúlveda, Juan Benigno
A1 Trutschnig, W.
AB 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.
PB Springer
SN 1578-7303
YR 2020
FD 2020-11-19
LK https://hdl.handle.net/20.500.14352/7274
UL https://hdl.handle.net/20.500.14352/7274
LA eng
NO Ministerio de Ciencia e Innovación (MICINN)
NO Junta de Andalucía
NO WISS 2025 project IDA-lab Salzburg
DS Docta Complutense
RD 17 abr 2025