scholarly journals Matrix transformations of strongly convergent sequences into Vσ

Filomat ◽  
2010 ◽  
Vol 24 (3) ◽  
pp. 103-109 ◽  
Author(s):  
S.A. Mohiuddine ◽  
M. Aiyub
Keyword(s):  
Matrix Transformations ◽  
Matrix Classes ◽  
The Matrix ◽  
Bounded Sequences ◽  
Convergent Sequences

In this paper, we define the spaces ?(p, s) and ?p (s), where ?(p, s) = {x:1/n? k=1 K-s |xk -?|pk ? 0 for some ?, s ? 0} and if pk = p for each k, we have ?(p, s)=?p(s). We further characterize the matrix classes (?(p, s), V? ), (?p (s), V? ) and (?p (s), V? )reg , where V? denotes the set of bounded sequences all of whose ?-mean are equal.

Matrix Transformations in an Incomplete Space

1968 ◽  
Vol 20 ◽  
pp. 727-734 ◽  
Author(s):  
I. J. Maddox
Keyword(s):  
Linear Space ◽  
Cauchy Sequence ◽  
Convergent Sequence ◽  
Convergent Series ◽  
Matrix Transformations ◽  
Cauchy Sequences ◽  
Complex Linear ◽  
Incomplete Space ◽  
Bounded Sequences ◽  
Convergent Sequences

Let X = (X, p) be a seminormed complex linear space with zero θ. Natural definitions of convergent sequence, Cauchy sequence, absolutely convergent series, etc., can be given in terms of the seminorm p. Let us write C = C(X) for the set of all convergent sequences for the set of Cauchy sequences; and L∞ for the set of all bounded sequences.

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 On the Domain of the Triangle on the Spaces of Null, Convergent, and Bounded Sequences

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Naim L. Braha ◽  
Feyzi Başar
Keyword(s):  
Type Theorem ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Topological Properties ◽  
Inclusion Relations ◽  
Bounded Sequences ◽  
Convergent Sequences

We introduce the spaces of -null, -convergent, and -bounded sequences. We examine some topological properties of the spaces and give some inclusion relations concerning these sequence spaces. Furthermore, we compute -, -, and -duals of these spaces. Finally, we characterize some classes of matrix transformations from the spaces of -bounded and -convergent sequences to the spaces of bounded, almost convergent, almost null, and convergent sequences and present a Steinhaus type theorem.

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 Almost convergence and some matrix transformations

Filomat ◽  
2007 ◽  
Vol 21 (2) ◽  
pp. 261-266 ◽  
Author(s):  
Q Qamaruddin ◽  
S.A. Mohiuddine
Keyword(s):  
Matrix Transformations ◽  
Almost Convergence ◽  
Matrix Classes ◽  
The Matrix

In this paper we characterize the matrix classes (l(p, u),??) and (l(p, u), ?) which generalize the matrix classes given by Mursaleen [6]. .

scholarly journals A Note on The Abel Matrix Transformations

2016 ◽  
Vol 4 (1) ◽  
pp. 48-53
Author(s):  
Mulatu Lemma ◽  
Latrice Tanksley ◽  
Keisha Brown
Keyword(s):  
Matrix Transformations ◽  
Main Research ◽  
Research Questions ◽  
Bounded Sequences ◽  
Convergent Sequences ◽  
Divergent Sequences

The purpose of this research is to investigate the effect of applying At to convergent sequences, bounded sequences, divergent sequences, and absolutely convergent sequences. We considering and answer the following interesting main research questions.

scholarly journals Measure of noncompactness for compact matrix operators on some BK spaces

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 1081-1086 ◽  
Author(s):  
A. Alotaibi ◽  
E. Malkowsky ◽  
M. Mursaleen
Keyword(s):  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Linear Operators ◽  
Matrix Transformations ◽  
Hausdorff Measure Of Noncompactness ◽  
Bounded Linear ◽  
Matrix Classes ◽  
The Matrix ◽  
Matrix Operators ◽  
Bk Spaces

In this paper, we characterize the matrix classes (?1, ??p )(1? p < 1). We also obtain estimates for the norms of the bounded linear operators LA defined by these matrix transformations and find conditions to obtain the corresponding subclasses of compact matrix operators by using the Hausdorff measure of noncompactness.

scholarly journals Matrix transformations involving certain Banach space valued sequence spaces

2000 ◽  
Vol 31 (2) ◽  
pp. 85-100
Author(s):  
J. K. Srivastava ◽  
B. K. Srivastava
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Linear Operators ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Matrix Classes ◽  
The Matrix ◽  
Matrix Class

In this paper for Banach spaces $X$ and $Y$ we characterize matrix classes $ (\Gamma (X,\lambda)$, $ l_\infty(Y,\mu))$, $ (\Gamma(X,\lambda),C(Y,\mu))$, $ (\Gamma(X,\lambda)$, $ c_0(Y,\mu))$, $ (\Gamma(X,\lambda)$, $ \Gamma^*(Y,\mu))$, $ (l_1(X,\lambda)$, $ \Gamma(Y,\mu))$ and $ (c_0(X,\lambda)$, $ c_0(Y,\mu))$ of bounded linear operators involving $ X$- and $ Y$-valued sequence spaces. Further as an application of the matrix class $ (c_0(X,\lambda)$, $ c_0(Y,\mu))$ we investigate the Banach space $ B(c_0(X,\lambda)$, $ c_0(Y,\mu))$ of all bounded linear mappings of $ c_0(x,\lambda)$ to $ c_0(Y,\mu)$.

scholarly journals Some matrix transformations and almost convergence

2013 ◽  
Vol 8 (2) ◽  
pp. 89-92 ◽  
Author(s):  
Neyaz Ahmad Sheikh ◽  
Ab. Hamid Ganie
Keyword(s):  
Sequence Space ◽  
Matrix Transformations ◽  
Almost Convergence ◽  
Infinite Matrices ◽  
Engineering And Technology ◽  
Bounded Sequences ◽  
Convergent Sequences

The sequence space bv(u,p) has been defined and the classes (bv(u,p):l?), (bv(u,p):c),and (bv(u,p):c0) of infinite matrices have been characterized by Ba?ar, Altay and Mursaleen ( see, [2] ). The main purposes of the present paper is to characterize the classes (bv(u,p):ƒ?),(bv(u, p):ƒ), and (bv(u,p):ƒ0), where ƒ?, ƒ, and ƒ0 denotes the spaces of almost bounded sequences, almost convergent sequences and almost convergent null sequences, respectively, with real or complex terms. Kathmandu University Journal of Science, Engineering and Technology Vol. 8, No. II, December, 2012, 89-92 DOI: http://dx.doi.org/10.3126/kuset.v8i2.7330

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