A characterization of (I, J)-regular matrices

2020/10/29 by Jeff Connor, Connor, Jeff, Paolo Leonetti +1
Computer Science · Mathematics · #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2010.16054

openalex publication_date 2020/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• A family of quotient maps of ℓ^∞ that do not admit uniformly continuous right inverses

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