scholarly journals Matrix Transformations between Certain Sequence Spaces over the Non-Newtonian Complex Field

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Uğur Kadak ◽  
Hakan Efe
Keyword(s):  
Linear Operator ◽  
Sufficient Conditions ◽  
Sequence Spaces ◽  
General Linear ◽  
Matrix Transformations ◽  
Infinite Matrix ◽  
Complex Field ◽  
Infinite Matrices ◽  
The Matrix ◽  
Necessary And Sufficient

In some cases, the most general linear operator between two sequence spaces is given by an infinite matrix. So the theory of matrix transformations has always been of great interest in the study of sequence spaces. In the present paper, we introduce the matrix transformations in sequence spaces over the fieldC*and characterize some classes of infinite matrices with respect to the non-Newtonian calculus. Also we give the necessary and sufficient conditions on an infinite matrix transforming one of the classical sets overC*to another one. Furthermore, the concept for sequence-to-sequence and series-to-series methods of summability is given with some illustrated examples.

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 generalized Riesz B-difference sequence spaces

Filomat ◽  
2010 ◽  
Vol 24 (4) ◽  
pp. 35-52 ◽  
Author(s):  
Metin Başarir
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Difference Sequence ◽  
Topological Properties ◽  
Linear Spaces ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
Difference Sequence Spaces

In this paper, we define the new generalized Riesz B-difference sequence spaces rq? (p, B), rqc (p, B), rq0 (p, B) and rq (p, B) which consist of the sequences whose Rq B-transforms are in the linear spaces l?(p), c (p), c0(p) and l(p), respectively, introduced by I.J. Maddox[8],[9]. We give some topological properties and compute the ?-, ?- and ?-duals of these spaces. Also we determine the necessary and sufficient conditions on the matrix transformations from these spaces into l? and c.

scholarly journals Summability, Some Sequence, Some Sequence Spaces and Their Matrix Transformations

2015 ◽  
Vol 1 (1) ◽  
pp. 29-35
Author(s):  
Suresh Ray ◽  
Shailendra Kumar Shrestha
Keyword(s):  
Linear Operator ◽  
Sequence Space ◽  
Academic Research ◽  
Sequence Spaces ◽  
General Linear ◽  
Matrix Transformations ◽  
Infinite Matrix

The most general linear operator to transform from new sequence space into another sequence space is actually given by an infinite matrix. In the present paper we represent some sequence spaces and their matrix transformations and summability.Journal of Advanced Academic Research Vol.1(1) 2014: 29-35

scholarly journals Nonnegative Infinite Matrices that Preserve (p,q)-Convexity of Sequences

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Chikkanna R. Selvaraj ◽  
Suguna Selvaraj
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Matrix Transformations ◽  
Infinite Matrix ◽  
Infinite Matrices ◽  
Necessary And Sufficient

This paper deals with matrix transformations that preserve the (p,q)-convexity of sequences. The main result gives the necessary and sufficient conditions for a nonnegative infinite matrix A to preserve the (p,q)-convexity of sequences. Further, we give examples of such matrices for different values of p and q.

scholarly journals A note on Köthe-Toeplitz duals of certain sequence spaces and their matrix transformations

1995 ◽  
Vol 18 (4) ◽  
pp. 681-688 ◽  
Author(s):  
B. Choudhary ◽  
S. K. Mishra
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Necessary And Sufficient

In this paper we define the sequence spacesSℓ∞(p),Sc(p)andSc0(p)and determine the Köthe-Toeplitz duals ofSℓ∞(p). We also obtain necessary and sufficient conditions for a matrixAto mapSℓ∞(p)toℓ∞and investigate some related problems.

scholarly journals Matrix Mappings on the Domains of Invertible Matrices

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Muhammed Altun
Keyword(s):  
Sufficient Conditions ◽  
Sequence Spaces ◽  
Banach Sequence Spaces ◽  
The Matrix ◽  
Matrix Domains ◽  
Necessary And Sufficient ◽  
Invertible Matrices ◽  
Matrix Operators ◽  
Banach Sequence

We focus on sequence spaces which are matrix domains of Banach sequence spaces. We show that the characterization of a random matrix operator , where and are matrix domains with invertible matrices and , can be reduced to the characterization of the operator . As an application, the necessary and sufficient conditions for the matrix operators between invertible matrix domains of the classical sequence spaces and norms of these operators are given.

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 New matrix domain derived by the matrix product

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1233-1241
Author(s):  
Vatan Karakaya ◽  
Necip Imşek ◽  
Kadri Doğan
Keyword(s):  
Topological Structure ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Matrix Transformation ◽  
Matrix Product ◽  
Difference Matrix ◽  
Matrix Domain ◽  
The Matrix ◽  
Necessary And Sufficient

In this work, we define new sequence spaces by using the matrix obtained by product of factorable matrix and generalized difference matrix of order m. Afterward, we investigate topological structure which are completeness, AK-property, AD-property. Also, we compute the ?-, ?- and ?- duals, and obtain bases for these sequence spaces. Finally we give necessary and sufficient conditions on matrix transformation between these new sequence spaces and c,??.

scholarly journals Matrix transformations between the sequence space BVP and certain BK spaces

2002 ◽  
Vol 123 (27) ◽  
pp. 33-46 ◽  
Author(s):  
Eberhard Malkowsky ◽  
Vladimir Rakocevic ◽  
Snezana Zivkovic-Zlatanovic
Keyword(s):  
Linear Operator ◽  
Hausdorff Measure ◽  
Sequence Space ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Matrix Transformations ◽  
Hausdorff Measure Of Noncompactness ◽  
Necessary And Sufficient ◽  
Bk Spaces

In this paper, we characterize matrix transformations between the sequence space bvp (1 < p < ?) and certain BK spaces. Further?more, we apply the Hausdorff measure of noncompactness to give necessary and sufficient conditions for a linear operator between these spaces to be compact.

scholarly journals The application domain of difference type matrix D(r,0,s,0,t) on some sequence spaces

2020 ◽  
pp. 32-32
Author(s):  
Avinoy Paul ◽  
Binod Tripathy
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Application Domain ◽  
Topological Properties ◽  
Difference Type ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
Matrix Mappings

In this paper we introduce new sequence spaces with the help of domain of matrix D(r,0,s,0,t), and study some of their topological properties. Further, we determine ? and ? duals of the new sequence spaces and finally, we establish the necessary and sufficient conditions for characterization of the matrix mappings.

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