scholarly journals Measure of noncompactness of operators and matrices on the spacescandc0

2006 ◽  
Vol 2006 ◽  
pp. 1-5 ◽  
Author(s):  
Bruno De Malafosse ◽  
Eberhard Malkowsky ◽  
Vladimir Rakocevic
Keyword(s):  
Linear Operator ◽  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Hausdorff Measure Of Noncompactness ◽  
Necessary And Sufficient

In this note, using the Hausdorff measure of noncompactness, necessary and sufficient conditions are formulated for a linear operator and matrices between the spacescandc0to be compact. Among other things, some results of Cohen and Dunford are recovered.

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.

Hausdorff measure of noncompactness of matrix mappings on Cesàro spaces

2021 ◽  
Vol 39 (1) ◽  
pp. 157-167
Author(s):  
G. Canan Hazar Güleç ◽  
M. Ali Sarıgöl
Keyword(s):  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Hausdorff Measure Of Noncompactness ◽  
Cesàro Spaces ◽  
Operator Norms ◽  
Necessary And Sufficient ◽  
Matrix Mappings

In this study we establish some identities or estimates for operator norms and the Hausdorff measure of noncompactness of certain operators on spaces |C_{α}|_{k}, which have more recently been introduced in [14]. Further, by applying the Hausdorff measure of noncompactness, we establish the necessary and sufficient conditions for such operators to be compact and so the some well known results are generalized.

scholarly journals Compact Operators for Almost Conservative and Strongly Conservative Matrices

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
S. A. Mohiuddine ◽  
M. Mursaleen ◽  
A. Alotaibi
Keyword(s):  
Compact Operator ◽  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Compact Operators ◽  
Necessary And Sufficient Conditions ◽  
Hausdorff Measure Of Noncompactness ◽  
Matrix Classes ◽  
Necessary And Sufficient ◽  
Conservative Matrix

We obtain the necessary and sufficient conditions for an almost conservative matrix to define a compact operator. We also establish some necessary and sufficient (or only sufficient) conditions for operators to be compact for matrix classes(f,X), whereX=c,c0,l∞. These results are achieved by applying the Hausdorff measure of noncompactness.

scholarly journals Compact operators on some generalized mixed norm spaces

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 1019-1026
Author(s):  
A. Alotaibi ◽  
E. Malkowsky ◽  
H. Nergiz
Keyword(s):  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Compact Operators ◽  
Necessary And Sufficient Conditions ◽  
Mixed Norm ◽  
Hausdorff Measure Of Noncompactness ◽  
Mixed Norm Spaces ◽  
Necessary And Sufficient

We establish identities or estimates for the Hausdorff measure of noncompactness of operators from some generalized mixed norm spaces into any of the spaces c0, c, ?1, and [?1, ??]<m(?)>. Furthermore we give necessary and sufficient conditions for the operators in these cases to be compact. Our results are complementary to those in [1, 3, 13].

scholarly journals Some notes on matrix mappings and their Hausdorff measure of noncompactness

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 1059-1072 ◽  
Author(s):  
E. Malkowsky ◽  
F. Özger ◽  
A. Alotaibi
Keyword(s):  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Linear Operators ◽  
Matrix Transformations ◽  
Hausdorff Measure Of Noncompactness ◽  
Bounded Linear ◽  
Matrix Domains ◽  
Necessary And Sufficient ◽  
Matrix Mappings

We consider the sequence spaces s0?(?B), s(c)? (?B) and s?(?B) with their topological properties, and give the characterizations of the classes of matrix transformations from them into any of the spaces ?1, ?1, c0 and c. We also establish some estimates for the norms of bounded linear operators defined by those matrix transformations. Moreover, the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for a linear operator on the sets s0?(?B), s(c)?(?B) and s?(?B) to be compact. We also close a gap in the proof of the characterizations by various authors of matrix transformations on matrix domains.

scholarly journals Measures of noncompactness in (N¯qΔ)summable difference sequence spaces

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5459-5470
Author(s):  
Ishfaq Malik ◽  
Tanweer Jalal
Keyword(s):  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Operators ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Hausdorff Measure Of Noncompactness ◽  
Measures Of Noncompactness ◽  
Necessary And Sufficient ◽  
Difference Sequence Spaces

In this paper we first introduce N?q?summable difference sequence spaces and prove some properties of these spaces. We then obtain the necessary and sufficient conditions for infinite matrices A to map these sequence spaces into the spaces c,c0, and l?. Finally, the Hausdorff measure of noncompactness is then used to obtain the necessary and sufficient conditions for the compactness of the linear operators defined on these spaces.

scholarly journals On the solvability of systems of linear equations on commutative semigroup

2010 ◽  
Vol 43 (4) ◽  
Author(s):  
Nguyen Thi Thu Huyen ◽  
Nguyen Minh Tuan
Keyword(s):  
Linear Operator ◽  
Linear Space ◽  
Commutative Semigroup ◽  
Linear Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Operator Equations ◽  
Systems Of Linear Equations ◽  
Necessary And Sufficient ◽  
Linear Operator Equations

AbstractThis paper deals with the solvability of systems of linear operator equations in a linear space. Namely, the paper provides necessary and sufficient conditions for the operators under which certain kinds of systems of operator equations are solvable.

scholarly journals On the spectrum of ψ-contracting operators

2001 ◽  
Vol 14 (3) ◽  
pp. 303-308 ◽  
Author(s):  
Anwar A. Al-Nayef
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Continuous Linear Operator ◽  
Continuous Linear ◽  
Hausdorff Measure Of Noncompactness

The spectrum σ(A) of a continuous linear operator A:E→E defined on a Banach space E, which is contracting with respect to the Hausdorff measure of noncompactness, is investigated.

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

Filomat ◽  
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].

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