Regular matrices of unbounded linear operators: II
Abstract
Let I , J \mathcal {I}, \mathcal {J} be two ideals on ω \omega . We obtain explicit Silverman–Toeplitz type theorems on matrices A = ( A n , k : n , k ∈ ω ) A=(A_{n,k}: n,k \in \omega ) of linear operators from a Banach space X X to a Banach space Y Y , so that A A maps bounded I \mathcal {I} -convergent sequences to bounded J \mathcal {J} -convergent sequences, preserving the corresponding ideal limits through a given linear map T : X → Y T: X\to Y . In the case where X = Y = R X=Y=\mathbf {R} and T x = x Tx=x for all x ∈ R x \in \mathbf {R} , this answers an open question in [J. Math. Anal. Appl. 1 (2021), Paper No. 125374]. As byproducts, we obtain characterizations of several matrix classes and Köthe–Toeplitz
Fields of Study & Subjects
Approximation Theory and Sequence Spaces
Advanced Banach Space Theory
Advanced Harmonic Analysis Research
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 6
- Pages
- 2535–2547
- Publication date
- 14 January 2026
- Language
- EN