Generalized difference sequence spaces and their dual spaces (original) (raw)

On Köthe-Toeplitz duals of generalized difference sequence spaces

Bull. Malaysian Math. Sci. Soc, 2000

Abstract. In this paper, we define the sequence spaces)(,)(cmvmv" and,)(,)(N m co mv and give some topological properties, inclusion relations of these sequence spaces, compute their continuous and Köthe-Toeplitz duals. The results of this paper, in a particular case, ...

Paranormed Norlund Nᵗ- difference sequence spaces and their α-, β- and γ-duals

Proyecciones, 2023

Kizmaz [4] defined some difference spaces viz., ∞ (∆), c(∆) and c 0 (∆) and studied by Et and Colak [1] thoroughly. In this paper, Norlund N t-difference sequence spaces N t (c 0 , p, ∆), N t (c, p, ∆) and N t (∞ , p, ∆) contain the sequences whose N t ∆-transforms in c 0 , c and ∞ are defined and the paranormed linear structures are developed on these spaces. It has been shown that the spaces N t (c 0 , p, ∆), N t (c, p, ∆) & N t (∞ , p, ∆) are linearly isomorphic and are of nonabsolute type. Further, it is verified that N t (c, p, ∆), N t (c 0 , p, ∆) and N t (l ∞ , p, ∆) of non-absolute form are isomorphic to N t (c 0 , p), N t (c, p) and N t (∞ , p), respectively. Topological properties such as the completeness and the isomorphism are also discussed. Some inclusion relations among these spaces are also verified. Finally, the α-, β-and γ-dual of these spaces are determined and constructed the Schauder-basis of N t (c 0 , p, ∆) and N t (c, p, ∆).

On a Generalized Difference Sequence Space

2021

In this work using the generalized difference operator ∆m, we generalize the sequence space m (φ) to sequence space m (φ, p, β) (∆m), give some topological properties about this space and show that the space m (φ, p, β) (∆m) is a BK−space by a suitable norm. The results obtained generalizes some known results.

A new type of difference sequence spaces

Thai Journal of Mathematics

In this paper we introduce the notion of the difference operator k m x ∆ for a fixed m ∈ N. We define the sequence spaces ( ) ( ) ( ) ( ) N m c and c m o m m ∈ ∆ ∆ ∆ ∞ , l

On Some Generalized Difference Sequence Spaces

2010

The main aim of this article is to introduce a new class of difference sequence spaces associated with a multiplier sequence which are isomorphic with the classical spaces c0, c and � ∞ respectively and investigate some algebraic and topological structures of the spaces. Mathematics Subject Classification: 40A05, 40C05, 46A45

On Certain Difference Sequence Spaces

The difference sequence spaces, and were introduced by Kizmaz (Can. Math. Bull. 24:169-176, 1981). In this paper, I introduce the sequence spaces and first difference sequence spaces.

On some new difference sequence spaces of non-absolute type

Mathematical and Computer Modelling, 2010

In the present paper, we introduce the spaces c λ 0 (∆) and c λ (∆) of difference sequences which are the BK -spaces of non-absolute type and prove that these spaces are linearly isomorphic to the spaces c 0 and c, respectively. We also derive some inclusion relations.

On Some New Generalized Difference Sequence Spaces of Nonabsolute Type

Journal of Mathematics, 2014

We define a new triangle matrix̂= ( ) by the composition of the matrices Λ = ( ) and ( , , ). Also, we introduce the sequence spaces 0 (̂), (̂), ℓ ∞ (̂), and ℓ (̂) by using matrix domain of the matrix̂on the classical sequence spaces 0 , , ℓ ∞ , and ℓ , respectively, where 1 ≤ < ∞. Moreover, we show that the space (̂) is norm isomorphic to for ∈ { 0 , , ℓ ∞ , ℓ }. Furthermore, we establish some inclusion relations concerning those spaces and determine -, -, and -duals of those spaces and construct the Schauder bases 0 (̂), (̂), and ℓ (̂). Finally, we characterize the classes ( 1 (̂) : 2 ) of infinite matrices where 1 ∈ { , 0 , ℓ } and 2 ∈ {ℓ ∞ , , 0 , ℓ }.