A characterization of (I, J)-regular matrices

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:504

Article

Connor, Jeff¹  Leonetti, Paolo² 

[1] Ohio Univ, Dept Math, Athens, OH 45701 USA

[2] Univ Bocconi, Dept Stat, Via Roentgen 1, I-20156 Milan, Italy

关键词: Ideal and statistical convergence;    Summability;    Regular matrices;    Convergent sequences;   

DOI  :  10.1016/j.jmaa.2021.125374

来源: Elsevier

【 摘 要 】

Let I, J be two ideals on N which contain the family Fin of finite sets. We provide necessary and sufficient conditions on the entries of an infinite real matrix A = (a(n, k)) which maps I-convergent bounded sequences into J-convergent bounded sequences and preserves the corresponding ideal limits. The well-known characterization of regular matrices due to Silverman-Toeplitz corresponds to the case I = J = Fin. Lastly, we provide some applications to permutation and diagonal matrices, which extend several known results in the literature. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free