Domain of generalized difference operator Δi3 of order three on the hahn sequence space h and matrix transformations. Issue 22 (21st December 2022)

• Record Type: Journal Article
• Authors: Tuǧ, Orhan; Rakočević, Viladimir; Malkowsky, Eberhard
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 22(2022)
• Page Start: 7433
• Page End: 7451
• Publication Date: 2022-12-21
• Subjects: Matrix domain -- generalized difference matrix of order three -- Hahn sequence space -- alpha- -- beta- and gamma-duals -- matrix transformations; 46A45 -- 40C05; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2021.1991875
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : In this article, domain of the third order generalized difference operator Δ i 3 in Hahn sequence space h is introduced. Some topological properties and inclusion relations are shown. Additionally, Schauder basis of the new Hahn sequence space h ( Δ i 3 ) is calculated and α −, β − and γ − dual of the space h ( Δ i 3 ) are computed. In the last section, some new matrix classes ( h ; b v ), ( h ; b v p ), ( h ; b v ∞ ), ( h ; b s ), ( h ; c s ), ( b v ; h ), ( b v 0 ; h ), ( b s ; h ), ( c s 0 ; h ), ( c s ; h ) are characterized. We conclude the paper with characterization of the classes ( h ( Δ i 3 ) ; μ ) and ( μ ; h ( Δ i 3 ) ) where μ = { c, c 0, ℓ 1, ℓ p, ℓ ∞, h, b s, c s, c s 0, b v, b v 0 } .