Bernal González, L.Fernández Sánchez, JuanSeoane Sepúlveda, Juan BenignoTrutschnig, W.2023-06-172023-06-172020-11-191578-730310.1007/s13398-020-00934-zhttps://hdl.handle.net/20.500.14352/7274It 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.engjournal articlehttps://link.springer.com/article/10.1007/s43037-020-00103-9open access512.64517LineabilityAlgebrabilityLatticeabilityMatrix summabilityÁlgebraAnálisis matemático1201 Álgebra1202 Análisis y Análisis Funcional