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 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 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 Matrix transformations and application to perturbed problems of some sequence spaces equations with operators

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 5123-5130
Author(s):  
Malafosse de ◽  
Ali Fares ◽  
Ali Ayad
Keyword(s):  
Linear Space ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Real Numbers ◽  
Positive Real ◽  
Complex Sequences ◽  
Perturbed Equation

Given any sequence z = (zn)n?1 of positive real numbers and any set E of complex sequences, we write Ez for the set of all sequences y = (yn)n?1 such that y/z = (yn/zn)n?1 ? E; in particular, cz = s(c) z denotes the set of all sequences y such that y/z converges. Starting with the equation Fx = Fb we deal with some perturbed equation of the form ? + Fx = Fb, where ? is a linear space of sequences. In this way we solve the previous equation where ? =(Ea)T and (E,F) ? {(l?,c), (c0,l?), (c0,c), (lp,c), (lp,l?), (w0,l?)} with p ? 1, and T is a triangle.

scholarly journals Vector-valued sequence spaces generated by infinite matrices

2001 ◽  
Vol 26 (9) ◽  
pp. 547-560
Author(s):  
Nandita Rath
Keyword(s):  
Sequence Spaces ◽  
Infinite Matrix ◽  
Real Sequence ◽  
Normed Spaces ◽  
Infinite Matrices ◽  
Positive Real ◽  
The Matrix ◽  
Almost All ◽  
Vector Valued

LetA=(ank)be an infinite matrix with allank≥0andPa bounded, positive real sequence. For normed spacesEandEkthe matrixAgenerates paranormed sequence spaces such as[A,P]∞((Ek)),[A,P]0((Ek)), and[A,P](E)which generalize almost all the existing sequence spaces, such asl∞,c0,c,lp,wp, and several others. In this paper, conditions under which these three paranormed spaces are separable, complete, andr-convex, are established.

scholarly journals Topological properties and matrix transformations of certain ordered generalized sequence spaces

1995 ◽  
Vol 18 (2) ◽  
pp. 341-356 ◽  
Author(s):  
Manjul Gupta ◽  
Kalika Kaushal
Keyword(s):  
Sequence Space ◽  
Topological Structure ◽  
Necessary Conditions ◽  
Riesz Space ◽  
Linear Operators ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Topological Properties ◽  
Vector Valued ◽  
Locally Convex

In this note, we carry out investigations related to the mixed impact of ordering and topological structure of a locally convex solid Riesz space(X,τ)and a scalar valued sequence spaceλ, on the vector valued sequence spaceλ(X)which is formed and topologized with the help ofλandX, and vice versa. Besides,we also characterizeo-matrix transformations fromc(X),ℓ∞(X)to themselves,cs(X)toc(X)and derive necessary conditions for a matrix of linear operators to transformℓ1(X)into a simple ordered vector valued sequence spaceΛ(X).

scholarly journals Onk-nearly uniform convex property in generalized Cesàro sequence spaces

2003 ◽  
Vol 2003 (57) ◽  
pp. 3599-3607 ◽  
Author(s):  
Winate Sanhan ◽  
Suthep Suantai
Keyword(s):  
Sequence Space ◽  
Bounded Sequence ◽  
Sequence Spaces ◽  
Luxemburg Norm ◽  
Real Numbers ◽  
Positive Real ◽  
Generalized Cesáro Sequence Space ◽  
Convex Property

We define a generalized Cesàro sequence spaceces(p), wherep=(pk)is a bounded sequence of positive real numbers, and consider it equipped with the Luxemburg norm. The main purpose of this paper is to show thatces(p)isk-nearly uniform convex (k-NUC) fork≥2whenlimn→∞infpn>1. Moreover, we also obtain that the Cesàro sequence spacecesp(where 1<p<∞)isk-NUC,kR, NUC, and has a drop property.

scholarly journals Approximation numbers of matrix transformations and inclusion maps

2011 ◽  
Vol 42 (2) ◽  
pp. 193-203
Author(s):  
M. Gupta ◽  
L. R. Acharya
Keyword(s):  
Banach Space ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Diagonal Operator ◽  
Approximation Numbers ◽  
Vector Valued

In this paper we establish relationships of the approximation numbers of matrix transformations acting between the vector-valued sequence spaces spaces of the type $\lambda(X)$ defined corresponding to a scalar-valued sequence space $\lambda$ and a Banach space $(X,\|.\|)$ as $$\lambda(X)=\{\overline x=\{x_i\}: x_i\in X, \forall~i\in \mathbb{N},~\{\|x_i\|_X\}\in \lambda\};$$ with those of their component operators. This study leads to a characterization of a diagonal operator to be approximable. Further, we compute the approximation numbers of inclusion maps acting between $\ell^p(X)$ spaces for $1\leq p\leq \infty$.

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 The Hahn Sequence Space Defined by the Cesáro Mean

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Murat Kirişci
Keyword(s):  
Banach Space ◽  
Sequence Space ◽  
Matrix Transformations ◽  
Space Theory ◽  
Topological Properties ◽  
Cesàro Mean ◽  
First Order ◽  
Inclusion Relations ◽  
The Matrix ◽  
Cesaro Mean

The -space of all sequences is given as such that converges and is a null sequence which is called the Hahn sequence space and is denoted by . Hahn (1922) defined the space and gave some general properties. G. Goes and S. Goes (1970) studied the functional analytic properties of this space. The study of Hahn sequence space was initiated by Chandrasekhara Rao (1990) with certain specific purpose in the Banach space theory. In this paper, the matrix domain of the Hahn sequence space determined by the Cesáro mean first order, denoted by , is obtained, and some inclusion relations and some topological properties of this space are investigated. Also dual spaces of this space are computed and, matrix transformations are characterized.

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