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1. Measures of Noncompactness in (N̅qΔ −) Summable Difference Sequence Spaces.

Author

Malik, I. Ahmad and Jalal, T.

Subjects
MATHEMATICS, MATRIX analytic methods, LINEAR operators, MAPS, NONLINEAR operators
Abstract

In this paper we first introduce N̅qΔ − summable difference sequence spaces and prove some properties of these spaces. We then obtain the necessary and sufficient conditions for infinite matrix A to map these sequence spaces on 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. [ABSTRACT FROM AUTHOR]

Published
2019

2. Measure of Noncompactness of Linear Operators between Spaces of Sequences That Are ( N,q) Summable or Bounded.

Author

Malkowsky, E. and Rakocevic, V.

Abstract

In this paper we investigate linear operators between arbitrary BK spaces X and spaces Y of sequences that are $${\text{(}}\bar N,q)$$ summable or bounded. We give necessary and sufficient conditions for infinite matrices A to map X into Y. Further, the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for A to be a compact operator. [ABSTRACT FROM AUTHOR]

Published
2001
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3. ON SOME DIFFERENCE SEQUENCE SPACES OF WEIGHTED MEANS AND COMPACT OPERATORS.

Author

Bas¸arir, Metin and Kara, Emrah Evren

Subjects
*SEQUENCE spaces, *COMPACT operators, *SCHAUDER bases, *MATHEMATICAL mappings, *HAUSDORFF measures, *HAUSDORFF compactifications
Abstract

In the peresent paper, by using generalized weighted mean and difference matrix of order m, we introduce the sequence spaces X(u, v,∇(m)), where X is one of the spaces l∞, c or c0. Also, we determine the α-,β- and -γduals of those spaces and construct their Schauder bases for X ∈ {l∞c, c0}. Morever, we give the characterization of the matrix mappings on the spaces l∞(u, v,∇m) for X ∈ {l∞, c, c0}. Finally, we characterize some classes of compact operators on the spaces l(u, v,∇m) and c0(u, v,∇m) by using the Hausdorff measure of noncompactness. [ABSTRACT FROM AUTHOR]

Published
2011

4. On Absolute Norlund Spaces and Matrix Operators

Author

M. Ali Sarigöl and G. Canan Hazar

Subjects
Pure mathematics, Series (mathematics), Applied Mathematics, General Mathematics, Operator (physics), 010102 general mathematics, 010103 numerical & computational mathematics, matrix transformations, Operator theory, Space (mathematics), Base (topology), absolute Nörlund summability, 01 natural sciences, Sequence spaces, dual spaces, Set (abstract data type), Matrix (mathematics), bounded linear operator, transformations, BK spaces, absolute Norlund summability, matrix, Order (group theory), 0101 mathematics, Mathematics
Abstract

In a more recent paper, the second author has introduced a space |C α | k as the set of all series by absolute summable using Cesaro matrix of order α > −1. In the present paper we extend it to the absolute Norlund space |N | k taking Norlund matrix in place of Cesaro matrix, and also examine some topological structures, α-β-γ-duals and the Schauder base of this space. Further we characterize certain matrix operators on that space and determine their operator norms, and so extend some well-known results.

Published
2018

5. Regularity Versus Compactness.

Author

Malkowsky, E.

Subjects
HAUSDORFF measures, LINEAR operators, HAUSDORFF spaces, COMPACT operators, SEQUENCE spaces, SCHAUDER bases
Abstract

A well-known result by Cohen and Dunford ([1], 1937) characterizes the class of all bounded linear operators from the space of all convergent complex sequences into itself. It follows that a regular matrix transformation cannot be compact. We use the theory of BK spaces and the Hausdorff measure of noncompactness to present a new proof for these results and establish their extensions to the spaces of strongly summable and strongly convergent sequences, and of convergent series. [ABSTRACT FROM AUTHOR]

Published
2021

6. operators

Author

Sarigol, MA

Subjects
Sequence spaces, BK spaces, Absolute summability, Continuous linear, functional
Abstract

In the present paper, we establish general representations of continuous linear functionals, which play important roles in Functional Analysis, of the absolute weighted spaces which have recently been introduced in Sarigol (2016, 2011), and also determine their norms. Further making use of this we give adjoint operators of matrix mappings defined on these spaces. (C) 2017 Ivane Javakhishvili Tbilisi State University. Published by Elsevier B.V.

Published
2018

7. Absolute CesA ro Series Spaces and Matrix Operators

Author

Hazar, GC and Sarigol, MA

Subjects
Dual spaces, BK spaces, Sequence spaces, Absolute Cesaro summability, Matrix transformations
Abstract

In this paper we derive a series space using the well known absolute CesA ro summability of Das (Proc. Camb. Philol. Soc. 67:321-326, 1970), compute its -dual, give some algebraic and topological properties, and characterize some matrix operators defined on that space. So we generalize some results of Bosanquet (J. Lond. Math. Soc. 20:39-48, 1945), Flett (Proc. Lond. Math. Soc. 7:113-141, 1957), Mehdi (Proc. Lond. Math. Soc. (3)10:180-199, 1960), Mazhar (Tohoku Math. J. 23:433-451, 1971), Orhan and SarA +/- gol (Rocky Mt. J. Math. 23(3):1091-1097, 1993) and SarA +/- gol (Commun. Math. Appl. 7(1):11-22, 2016; Math. Comput. Model. 55:1763-1769, 2012).

Published
2018

8. Representations of functionals on absolute weighted spaces and adjoint operators

Author

Mehmet Ali Sarıgöl

Subjects
Discrete mathematics, 0209 industrial biotechnology, Pure mathematics, Functional analysis, General Mathematics, Topological tensor product, lcsh:Mathematics, 010102 general mathematics, 02 engineering and technology, Operator theory, lcsh:QA1-939, 01 natural sciences, Sequence spaces, Continuous linear operator, Matrix (mathematics), 020901 industrial engineering & automation, Absolute (philosophy), BK spaces, Compact-open topology, Continuous linear functional, 0101 mathematics, Reflexive space, Absolute summability, Mathematics
Abstract

In the present paper, we establish general representations of continuous linear functionals, which play important roles in Functional Analysis, of the absolute weighted spaces which have recently been introduced in Sarıgöl (2016, 2011), and also determine their norms. Further making use of this we give adjoint operators of matrix mappings defined on these spaces. Keywords: Sequence spaces, BK spaces, Absolute summability, Continuous linear functional

Published
2018