Abstract
In the present study, we introduce a new RH-regular 4D (4-dimensional) matrix derived by Jordan’s function and define double sequence spaces by using domains of 4D Jordan totient matrixJton some classical double sequence spaces. Also, theα-,βϑ-, andγ-duals of these spaces are determined. Finally, some classes of 4D matrices on these spaces are characterized.
Highlights
Introduction and PreliminariesThe Jordans’s function Jt : N ⟶ N, k ⟼ JtðkÞ is described as the number of t-tuples of positive integers all less than or equal to k that form a coprime with ðt + 1Þ-tuples together with k, where k, t ∈ N and N = f1, 2, ⋯g
We introduce a new RH-regular 4D (4-dimensional) matrix derived by Jordan’s function and define double sequence spaces by using domains of 4D Jordan totient matrix Jt on some classical double sequence spaces
We introduce the double sequence spaces by using the domains of 4D Jordan totient matrix Jt as follows: Jt∞
Summary
The set of all regularly convergent double sequences is represented by Cr, and Mu, Cbp, and Cr are Banach spaces with the norm kxk∞ = supk,l∈Njxklj. The spaces of all almost convergent and almost null double sequences denoted by C f and C f0 , respectively. The domain ΨðBθÞ of a 4D complex infinite matrix B in a double sequence space Ψ consists of the sequences whose B-transforms are in Ψ; that is,. The 2D Jordan matrix and its domain on the space of lp of absolutely p-summable single sequences are described and examined by I. lkhan et al [5]. The 4D Euler-totient matrix Φ⋆ and domains of this matrix on double sequences Ls, Mu, Cp, Cbp, and Cr were described and examined by Demiriz and Erdem [6] and Erdem and Demiriz [7].
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