Matrix Mappings on the Domains of Invertible Matrices

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.

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

Yugoslav journal of operations research ◽

10.2298/yjor200618032p ◽

2020 ◽

pp. 32-32

Author(s):

Avinoy Paul ◽

Binod Tripathy

Keyword(s):

Sufficient Conditions ◽

Sequence Spaces ◽

Application Domain ◽

Topological Properties ◽

Difference Type ◽

The Matrix ◽

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.

On some new paranormed sequence spaces defined by the matrix (D )(r,0,0,s)

Proyecciones (Antofagasta) ◽

10.22199/issn.0717-6279-4321 ◽

2021 ◽

Vol 40 (3) ◽

pp. 779-796

Author(s):

Avinoy Paul

Keyword(s):

Sufficient Conditions ◽

Sequence Spaces ◽

Topological Properties ◽

The Matrix ◽

Matrix Mappings

In this paper, we introduce some new paranormed sequence spaces and study some topological properties. Further, we determine α, β and γ-duals of the new sequence spaces and finally, we establish the necessary and sufficient conditions for characterization of matrix mappings.

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

The Scientific World JOURNAL ◽

10.1155/2014/705818 ◽

2014 ◽

Vol 2014 ◽

pp. 1-12 ◽

Cited By ~ 8

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 ◽

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 generalized Riesz B-difference sequence spaces

Filomat ◽

10.2298/fil1004035b ◽

2010 ◽

Vol 24 (4) ◽

pp. 35-52 ◽

Cited By ~ 13

Author(s):

Metin Başarir

Keyword(s):

Sufficient Conditions ◽

Sequence Spaces ◽

Matrix Transformations ◽

Difference Sequence ◽

Topological Properties ◽

Linear Spaces ◽

The Matrix ◽

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.

The Schur and (weak) Dunford-Pettis properties in Banach lattices

Journal of the Australian Mathematical Society ◽

10.1017/s144678870000882x ◽

2002 ◽

Vol 73 (2) ◽

pp. 251-278 ◽

Cited By ~ 12

Author(s):

Anna Kamińska ◽

Mieczysław Mastyło

Keyword(s):

Orlicz Spaces ◽

Sufficient Conditions ◽

Complete Characterization ◽

Sequence Spaces ◽

Banach Lattices ◽

Schur Property ◽

Atomic Measure ◽

Orlicz Sequence Spaces ◽

AbstractWe study the Schur and (weak) Dunford-Pettis properties in Banach lattices. We show that l1, c0 and l∞ are the only Banach symmetric sequence spaces with the weak Dunford-Pettis property. We also characterize a large class of Banach lattices without the (weak) Dunford-Pettis property. In MusielakOrlicz sequence spaces we give some necessary and sufficient conditions for the Schur property, extending the Yamamuro result. We also present a number of results on the Schur property in weighted Orlicz sequence spaces, and, in particular, we find a complete characterization of this property for weights belonging to class ∧. We also present examples of weighted Orlicz spaces with the Schur property which are not L1-spaces. Finally, as an application of the results in sequence spaces, we provide a description of the weak Dunford-Pettis and the positive Schur properties in Orlicz spaces over an infinite non-atomic measure space.

Real Representation Approach to Quaternion Matrix Equation Involving ϕ-Hermicity

Mathematical Problems in Engineering ◽

10.1155/2019/3258349 ◽

2019 ◽

Vol 2019 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

Xin Liu ◽

Huajun Huang ◽

Zhuo-Heng He

Keyword(s):

Matrix Equation ◽

Sufficient Conditions ◽

Complete Characterization ◽

Quaternion Matrix ◽

Real Representation ◽

Quaternion Matrix Equation ◽

The Matrix ◽

Hermitian Solution ◽

For a quaternion matrix A, we denote by Aϕ the matrix obtained by applying ϕ entrywise to the transposed matrix AT, where ϕ is a nonstandard involution of quaternions. A is said to be ϕ-Hermitian or ϕ-skew-Hermitian if A=Aϕ or A=−Aϕ, respectively. In this paper, we give a complete characterization of the nonstandard involutions ϕ of quaternions and their conjugacy properties; then we establish a new real representation of a quaternion matrix. Based on this, we derive some necessary and sufficient conditions for the existence of a ϕ-Hermitian solution or ϕ-skew-Hermitian solution to the quaternion matrix equation AX=B. Moreover, we give solutions of the quaternion equation when it is solvable.

Characterization of some classes of compact operators between certain matrix domains of triangles

Filomat ◽

10.2298/fil1605327d ◽

2016 ◽

Vol 30 (5) ◽

pp. 1327-1337

Author(s):

Ivana Djolovic ◽

Eberhard Malkowsky

Keyword(s):

Hausdorff Measure ◽

Measure Of Noncompactness ◽

Sufficient Conditions ◽

Compact Operators ◽

Fredholm Operators ◽

Hausdorff Measure Of Noncompactness ◽

Matrix Domains ◽

Matrix Operators

In this paper, we characterize the classes ((?1)T, (?1)?T ) and (cT, c?T) where T = (tnk)?n,k=0 and ?T=(?tnk)?n,k=0 are arbitrary triangles. We establish identities or estimates for the Hausdorff measure of noncompactness of operators given by matrices in the classes ((?1)T, (?1)?T ) and (cT, c?T). Furthermore we give sufficient conditions for such matrix operators to be Fredholm operators on (?1)T and cT. As an application of our results, we consider the class (bv, bv) and the corresponding classes of matrix operators. Our results are complementary to those in [2] and some of them are generalization for those in [3].

New matrix domain derived by the matrix product

Filomat ◽

10.2298/fil1605233k ◽

2016 ◽

Vol 30 (5) ◽

pp. 1233-1241

Author(s):

Vatan Karakaya ◽

Necip Imşek ◽

Kadri Doğan

Keyword(s):

Topological Structure ◽

Sufficient Conditions ◽

Sequence Spaces ◽

Matrix Transformation ◽

Matrix Product ◽

Difference Matrix ◽

Matrix Domain ◽

The Matrix ◽

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,??.

The outer generalized inverse of an even-order tensor

Electronic Journal of Linear Algebra ◽

10.13001/ela.2020.5011 ◽

2020 ◽

Vol 36 (36) ◽

pp. 599-615

Author(s):

Jun Ji ◽

Yimin Wei

Keyword(s):

Generalized Inverse ◽

Sufficient Conditions ◽

Full Rank ◽

Outer Inverse ◽

The Matrix ◽

Even Order ◽

Rank Factorization ◽

Equivalent Conditions

Necessary and sufficient conditions for the existence of the outer inverse of a tensor with the Einstein product are studied. This generalized inverse of a tensor unifies several generalized inverses of tensors introduced recently in the literature, including the weighted Moore-Penrose, the Moore-Penrose, and the Drazin inverses. The outer inverse of a tensor is expressed through the matrix unfolding of a tensor and the tensor folding. This expression is used to find a characterization of the outer inverse through group inverses, establish the behavior of outer inverse under a small perturbation, and show the existence of a full rank factorization of a tensor and obtain the expression of the outer inverse using full rank factorization. The tensor reverse rule of the weighted Moore-Penrose and Moore-Penrose inverses is examined and equivalent conditions are also developed.

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences ◽

Optimally scalable matrices

10.1098/rsta.1977.0147 ◽

1977 ◽

Vol 287 (1345) ◽

pp. 307-349 ◽

Cited By ~ 1

Keyword(s):

Matrix Theory ◽

Sufficient Conditions ◽

Spectral Structure ◽

Combinatorial Matrix Theory ◽

Sign Distribution ◽

Special Cases ◽

The Matrix ◽

Singular Matrices ◽

The characterization of matrices which can be optimally scaled with respect to various modes of scaling is studied. Particular attention is given to the following two problems: ( a) The characterization of those square matrices for which inf lub (D -1 MD) D is attainable for some non-singular diagonal matrix D . ( b) The characterization of those square non-singular matrices A for which inf cond 12 (D 1 AD 2 ) D 1 , D 2 is attainable for some non-singular diagonal matrices D 1 and D 2 . For norms having certain properties, various necessary and sufficient conditions for optimal scalability are obtained when, in problem ( a ), the matrix A and, in problem ( b ), both A and A -1 have chequerboard sign distribution. The characterizations so established impose various conditions on the combinatorial and spectral structure of the matrices. These are investigated by using results from the Perron-Frobenius theory of non-negative matrices and combinatorial matrix theory. It is shown that the Holder or l p -norms have the required properties, and that, in general, the only norms having all of the properties needed, for both the necessary and the sufficient conditions to be satisfied, are variants of the l p -norms. For the special cases p = 1 and p = oo, the characterizations obtained hold for all matrices, irrespective of sign distribution.