On the spaces of Cesàro absolutelyp‐summable, null, and convergent sequences

Abstract

In this paper, we investigate some properties of the domains c0(Cn), c(Cn), and ℓp(Cn) with 0 < p < 1 of the Cesàro matrix of order n in the classical spaces c0, c, and ℓp of null, convergent, and absolutely p‐summable sequences, respectively, and compute the α‐, β‐, and γ‐duals of these spaces. We characterize the classes of infinite matrices from the space ℓp(Cn) to the spaces ℓ∞, c, and c0 and from a normed sequence spaces to the sequence spaces c0(Cn), c(Cn), and ℓp(Cn). Moreover, we compute the lower bound of operators from ℓp into ℓp(Cn), from ℓp(Cn) into ℓp and from ℓp(Cn) into itself.

Factorization of Cesàro operator and related inequalities

“…The Cesàro sequence space C 1 (p), its topological properties, its matrix transformations, and matrix domains are studied in [8,16]. Recently, the general case C n (p) and its topological properties, matrix transformations, and matrix domains for 0 < p < ∞ have been thoroughly studied [14,15]. Gamma matrix of order n. The measure…”

Upper Bound of Difference Operator on Some Matrix Domains

“…By using matrix domains of special triangular matrices in classical spaces, many authors have introduced and studied new Banach spaces. For the relevant literature, we refer to the papers [7,8,9,10,11,12,13] and textbook [14]. Recently, Roopaei has computed the norm of operators on several matrix domains in [2,15,16,17,18,19,20,21].…”

“…In [23], Ng and Lee introduced the Cesàro sequence spaces X p and X ∞ of non-absolute type as the domains of Cesàro matrix C 1 of order one in the spaces p and ∞ , where 1 ≤ p < ∞. Recently, Şengönül and Başar [24] studied the Cesàro sequence spaces c 0 and c of non-absolute type as the domains of Cesàro matrix C 1 of order one in the spaces c 0 and c, also Roopaei et al [25] and Roopaei and Başar [10] have investigated the Cesáro space C n p for p ≥ 1 and 0 < p < 1, respectively.…”

Binomial Operator as a Hausdorff Operator of the Euler Type

“…We use the notation ces(p) instead of ces(1, p) as the sequence space associated with the wellknown Cesàro matrix C. For more information about Cesàro matrix, the readers can refer to [20,19]. By letting dµ(θ) = αθ α−1 dθ in the definition of the Hausdorff matrix, the Gamma matrix of order α, Γ α = (γ α j,k ), is…”

“…Although topological properties and inclusion relations of b r,s (p) have largely been explored [4,13,12], computing the norm of binomial operators on sequence spaces has not been investigated to date. More recently, the author has computed the norm of operators on several sequence spaces, [7,8,21,22,14,15,16,17,18,20,19]. Several papers have published about the binomial sequence space, who is a matrix domain associated with the binomial operator or other spaces which obtain by this operator [4,5,11,24,23,6].…”