2015/01/06 by Serkan Demiriz, Demiriz, Serkan, Osman Duyar +1
Mathematics · #40C05 #46A45 #Advanced Banach Space Theory #Advanced Topics in Algebra #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:40C05 #msc:46A45
paper · pdf · doi:10.48550/arxiv.1501.01113
13 pages
arxiv created 2015/01/06 · openalex publication_date 2015/01/06 · arxiv updated 2015/01/07 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
In this study, we define the spaces Mu(Δ),Cp(Δ),C0p(Δ), Cr(Δ) and Lq(Δ) of double sequences whose difference transforms are bounded , convergent in the Pringsheim's sense, null in the Pringsheim's sense, both convergent in the Pringsheim's sense and bounded, regularly convergent and absolutely q-summable, respectively, and also examine some inclusion relations related to those sequence spaces. Furthermore, we show that these sequence spaces are Banach spaces . We determine the alpha-dual of the space Mu(Δ) and the β(v)-dual of the space Cη(Δ) of double sequences, where v,η∈ \p,bp,r\. Finally, we characterize the classes (μ:Cv(Δ)) for v∈ \p,bp,r\ of four dimensional matrix transformations, where μ is any given space of double sequences.