scholarly journals Domain of the Double Sequential Band Matrix in the Sequence Space

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Havva Nergiz ◽  
Feyzi Başar
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Schauder Basis ◽  
Matrix Transformations ◽  
Difference Matrix ◽  
Band Matrix ◽  
Alpha Beta

The sequence space was introduced by Maddox (1967). Quite recently, the domain of the generalized difference matrix in the sequence space has been investigated by Kirişçi and Başar (2010). In the present paper, the sequence space of nonabsolute type has been studied which is the domain of the generalized difference matrix in the sequence space . Furthermore, the alpha-, beta-, and gamma-duals of the space have been determined, and the Schauder basis has been given. The classes of matrix transformations from the space to the spaces ,candc0have been characterized. Additionally, the characterizations of some other matrix transformations from the space to the Euler, Riesz, difference, and so forth sequence spaces have been obtained by means of a given lemma. The last section of the paper has been devoted to conclusion.

scholarly journals Almost convergent sequence spaces derived by the domain of quadruple band matrix

2020 ◽  
Vol 19 (1) ◽  
pp. 155-170
Author(s):  
Mustafa Cemil Bişgin
Keyword(s):  
Convergent Sequence ◽  
Sequence Spaces ◽  
Schauder Basis ◽  
Third Order ◽  
Difference Matrix ◽  
Order Difference ◽  
Matrix Classes ◽  
Band Matrix ◽  
Almost Convergent Sequence ◽  
Triple Band

AbstractIn this work, we construct the sequence spaces f(Q(r, s, t, u)), f0(Q(r, s, t, u)) and fs(Q(r, s, t, u)), where Q(r, s, t, u) is quadruple band matrix which generalizes the matrices Δ3, B(r, s, t), Δ2, B(r, s) and Δ, where Δ3, B(r, s, t), Δ2, B(r, s) and Δ are called third order difference, triple band, second order difference, double band and difference matrix, respectively. Also, we prove that these spaces are BK-spaces and are linearly isomorphic to the sequence spaces f, f0 and fs, respectively. Moreover, we give the Schauder basis and β, γ-duals of those spaces. Lastly, we characterize some matrix classes related to those spaces.

scholarly journals ON GENERALIZED FIBONACCI DIFFERENCE SPACE DERIVED FROM THE ABSOLUTELY p− SUMMABLE SEQUENCE SPACES

2019 ◽  
pp. 903
Author(s):  
Gülsen Kılınç
Keyword(s):  
Sequence Space ◽  
Bounded Sequence ◽  
Sequence Spaces ◽  
The Other ◽  
Matrix Transformations ◽  
Real Numbers ◽  
Positive Real ◽  
Topological Features ◽  
Summable Sequence ◽  
Alpha Beta

In this study, it is specified \emph{the sequence space} $l\left( F\left( r,s\right),p\right) $, (where $p=\left( p_{k}\right) $ is any bounded sequence of positive real numbers) and researched some algebraic and topological features of this space. Further, $\alpha -,$ $\beta -,$ $\gamma -$ duals and its Schauder Basis are given. The classes of \emph{matrix transformations} from the space $l\left( F\left( r,s\right) ,p\right) $ to the spaces $l_{\infty },c,$ and $% c_{0}$ are qualified. Additionally, acquiring qualifications of some other \emph{matrix transformations} from the space $l\left( F\left( r,s\right) ,p\right) $ to the \emph{Euler, Riesz, difference}, etc., \emph{sequence spaces} is the other result of the paper.

scholarly journals Dual pairs of sequence spaces

2001 ◽  
Vol 28 (1) ◽  
pp. 9-23 ◽  
Author(s):  
Johann Boos ◽  
Toivo Leiger
Keyword(s):  
Sequence Space ◽  
Dual Pair ◽  
General Concept ◽  
Sequence Spaces ◽  
Dual Pairs ◽  
The Third ◽  
Convex Sequence ◽  
Starting Point ◽  
Alpha Beta ◽  
Locally Convex

The paper aims to develop for sequence spacesEa general concept for reconciling certain results, for example inclusion theorems, concerning generalizations of the Köthe-Toeplitz dualsE×(×∈{α,β})combined with dualities(E,G),G⊂E×, and theSAK-property (weak sectional convergence). TakingEβ:={(yk)∈ω:=𝕜ℕ|(ykxk)∈cs}=:Ecs, wherecsdenotes the set of all summable sequences, as a starting point, then we get a general substitute ofEcsby replacingcsby any locally convex sequence spaceSwith sums∈S′(in particular, a sum space) as defined by Ruckle (1970). This idea provides a dual pair(E,ES)of sequence spaces and gives rise for a generalization of the solid topology and for the investigation of the continuity of quasi-matrix maps relative to topologies of the duality(E,Eβ). That research is the basis for general versions of three types of inclusion theorems: two of them are originally due to Bennett and Kalton (1973) and generalized by the authors (see Boos and Leiger (1993 and 1997)), and the third was done by Große-Erdmann (1992). Finally, the generalizations, carried out in this paper, are justified by four applications with results around different kinds of Köthe-Toeplitz duals and related section properties.

scholarly journals On Domain of Nörlund Sequences

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 268 ◽  
Author(s):  
Kuddusi Kayaduman ◽  
Fevzi Yaşar
Keyword(s):  
Banach Space ◽  
Bounded Variation ◽  
Sequence Space ◽  
Convergent Series ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Nörlund Matrix ◽  
Inclusion Relations ◽  
The Matrix ◽  
New Space

In 1978, the domain of the Nörlund matrix on the classical sequence spaces lp and l∞ was introduced by Wang, where 1 ≤ p < ∞. Tuğ and Başar studied the matrix domain of Nörlund mean on the sequence spaces f0 and f in 2016. Additionally, Tuğ defined and investigated a new sequence space as the domain of the Nörlund matrix on the space of bounded variation sequences in 2017. In this article, we defined new space and and examined the domain of the Nörlund mean on the bs and cs, which are bounded and convergent series, respectively. We also examined their inclusion relations. We defined the norms over them and investigated whether these new spaces provide conditions of Banach space. Finally, we determined their α­, β­, γ­duals, and characterized their matrix transformations on this space and into this space.

On the factorable spaces of absolutely p-summable, null, convergent, and bounded sequences

2021 ◽  
Vol 71 (6) ◽  
pp. 1375-1400
Author(s):  
Feyzi Başar ◽  
Hadi Roopaei
Keyword(s):  
Lower Bound ◽  
Sequence Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Matrix Transformations ◽  
Infinite Matrix ◽  
The Matrix ◽  
Alpha Beta ◽  
Necessary And Sufficient ◽  
Bounded Sequences

Abstract Let F denote the factorable matrix and X ∈ {ℓp , c 0, c, ℓ ∞}. In this study, we introduce the domains X(F) of the factorable matrix in the spaces X. Also, we give the bases and determine the alpha-, beta- and gamma-duals of the spaces X(F). We obtain the necessary and sufficient conditions on an infinite matrix belonging to the classes (ℓ p (F), ℓ ∞), (ℓ p (F), f) and (X, Y(F)) of matrix transformations, where Y denotes any given sequence space. Furthermore, we give the necessary and sufficient conditions for factorizing an operator based on the matrix F and derive two factorizations for the Cesàro and Hilbert matrices based on the Gamma matrix. Additionally, we investigate the norm of operators on the domain of the matrix F. Finally, we find the norm of Hilbert operators on some sequence spaces and deal with the lower bound of operators on the domain of the factorable matrix.

scholarly journals Some properties of Generalized Fibonacci difference bounded and $p$-absolutely convergent sequences

2018 ◽  
Vol 36 (1) ◽  
pp. 37 ◽  
Author(s):  
Bipan Hazarika ◽  
Anupam Das
Keyword(s):  
Sequence Space ◽  
Geometric Properties ◽  
Matrix Classes ◽  
Band Matrix ◽  
Inclusion Relations ◽  
Alpha Beta ◽  
Convergent Sequences

The main objective of this paper is to introduced a new sequence space $l_{p}(\hat{F}(r,s)),$ $ 1\leq p \leq \infty$ by using the band matrix $\hat{F}(r,s).$ We also establish a few inclusion relations concerning this space and determine its $\alpha-,\beta-,\gamma-$duals. We also characterize some matrix classes on the space $l_{p}(\hat{F}(r,s))$ and examine some geometric properties of this space.

scholarly journals On matrix transformations concerning the Nakano vector-valued sequence space

2001 ◽  
Vol 26 (11) ◽  
pp. 671-678
Author(s):  
Suthep Suantai
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Real Numbers ◽  
Positive Real ◽  
The Matrix ◽  
Vector Valued ◽  
Bounded Sequences

We give the matrix characterizations from Nakano vector-valued sequence spaceℓ(X,p)andFr(X,p)into the sequence spacesEr,ℓ∞,ℓ¯∞(q),bs, andcs, wherep=(pk)andq=(qk)are bounded sequences of positive real numbers such thatPk>1for allk∈ℕandr≥0.

scholarly journals Matrix transformations of some sequence spaces—II

1970 ◽  
Vol 11 (2) ◽  
pp. 162-166 ◽  
Author(s):  
K. Chandrasekhara Rao
Keyword(s):  
Vector Space ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Complex Numbers ◽  
Image Position

This paper is a continuation of [1]. We begin with the notations for the sequence spaces considered in this paper. Let Γ be the space of sequences x = {xp} of complex numbers such that |xp|1/p⃗0 as p⃗∞. Γ can also be regarded as the space of integral functions f(z) = . The sequence space Γ is a vector space over the complex numbers with seminorms

scholarly journals Applications of Measure of Noncompactness in Matrix Operators on Some Sequence Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
M. Mursaleen ◽  
A. Latif
Keyword(s):  
Hausdorff Measure ◽  
Sequence Space ◽  
Measure Of Noncompactness ◽  
Linear Operators ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Hausdorff Measure Of Noncompactness ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Matrix Operators

We determine the conditions for some matrix transformations fromn(ϕ), where the sequence spacen(ϕ), which is related to theℓpspaces, was introduced by Sargent (1960). We also obtain estimates for the norms of the bounded linear operators defined by these matrix transformations and find conditions to obtain the corresponding subclasses of compact matrix operators by using the Hausdorff measure of noncompactness.

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