Generalization of the Absolute Cesàro Space and Some Matrix Transformations. (4th July 2019)

• Record Type: Journal Article
• Authors: Gökçe, Fadime; Sarıgöl, Mehmet Ali
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 9(2019)
• Page Start: 1039
• Page End: 1052
• Publication Date: 2019-07-04
• Subjects: Absolute summability -- bounded operators -- Cesàro matrix -- matrix transformations -- sequence spaces; 40C05 -- 40F05 -- 46A45; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1596130
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The space ℓ k was extended to the space ℓ ( p ) by Maddox, where p = ( p n ) is a bounded sequence of positive numbers. The series space | C λ, μ | k has more recently been studied by Hazar and Sarıgöl. In this article, following Maddox we derived a more general series space | C λ, μ | ( p ) and show that it is a paranormed space and linearly isomorphic to the space ℓ ( p ) . Also, we construct its α −, β −, γ − duals and Schauder basis. Further, we characterize the classes of certain matrix transformations on that space and obtain some well-known results as a particular case.