Matrix transformations of Norlund–Orlicz difference sequence spaces of nonabsolute type and their Toeplitz duals

Abstract

In this paper, the Nörlund-Orlicz difference sequence space N t (F, m n , u, q) of nonabsolute type is introduced as a domain of Nörlund means which is isomorphic to the space (p) and the basis of the space is constructed. Additionally, the α-, β-, and γ-duals of the spaces are computed and their matrix transformations are given. Finally, the properties like rotundity, modularity of the newly formed spaces are established.

A note on Nakano generalized difference sequence space

“…Mursaleen and Noman [10] examined compact operators on some difference sequence spaces. Kiliçman and Raj [5] introduced the matrix transformations of Norlund-Orlicz difference sequence spaces of nonabsolute type. Yaying et al [15] investigated the matrix transformations on q-Cesáro sequence spaces of nonabsolute type.…”

“…If (r j ) ∈ ∞ , then (r, m n+1 ) = {w = (w j ) ∈ C N : ∞ j=0 | m n+1 |w j || r j < ∞}. Several geometric and topological characteristics of (r, m n+1 ) have been studied (see [5,16]). By B(W , Z) we de-note the set of all linear bounded operators between Banach spaces W and Z, and if W = Z, then we write B(W ).…”

“…On sequence spaces, Mursaleen and Noman [10] investigated the compact operators on some difference sequence spaces. Kiliçman and Raj [5] studied the matrix transformations of Norlund-Orlicz difference sequence spaces of nonabsolute type. Yaying et al [15] examined the operator ideal of type sequence space whose q-Cesáro matrix in p for all q ∈ (0, 1] and 1 < p < ∞.…”

Multiplication Operators on Orlicz Generalized Difference (sss)

“…When ψðwÞ = w r , then ℓ ψ ðΔ m n+1 Þ = ℓ r ðΔ m n+1 Þ investigated via many authors (see [19][20][21]). By BðW, ZÞ, we will denote the set of every operators which are linear and bounded between Banach spaces W and Z, and if W = Z, we write B ðWÞ.…”