Domain of the Nörlund Matrix in Some of Maddox’s Spaces
Proceedings of the National Academy of Sciences India Section A - Physical Sciences, cilt.87, sa.3, ss.363-371, 2017 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 87 Sayı: 3
- Basım Tarihi: 2017
- Doi Numarası: 10.1007/s40010-017-0359-4
- Dergi Adı: Proceedings of the National Academy of Sciences India Section A - Physical Sciences
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.363-371
- Anahtar Kelimeler: Paranormed sequence space, Matrix domain, alpha-, beta- and gamma-duals, Almost convergence, Matrix transformations
- Uşak Üniversitesi Adresli: Evet
Özet
Maddox defined the sequence spaces ℓ∞(p) , c(p) and c0(p) in Maddox (Q J Math Oxf Lond 18(2):345–355, 1967) and Maddox (Proc Comb Phil Soc 64:335–340, 1968), respectively. In the present paper, following Yeşilkayagil and Başar (Abstr Appl Anal, 2014), the Nörlund sequence spaces ℓ∞(Nt, p) , c(Nt, p) and c0(Nt, p) of non-absolute type are introduced and it is proved that those sequence spaces are linearly isomorphic to the spaces ℓ∞(p) , c(p) and c0(p) , respectively. The α-, β- and γ-duals of the spaces ℓ∞(Nt, p) , c(Nt, p) and c0(Nt, p) are determined and the bases of the spaces c(Nt, p) and c0(Nt, p) are given. Besides this, the classes of matrix transformations from ℓ∞(Nt, p) to ℓ∞, f, f0, c, c0 and from λ(p) to μ(Nt, p) are characterized, where λ, μ denote any of the classical sequence spaces ℓ∞, c or c0.