scholarly journals Matrix transformations related to I-convergent sequences

2019 ◽  
Vol 22 (2) ◽  
pp. 191-200
Author(s):  
Enno Kolk
Keyword(s):  
Linear Operators ◽  
Matrix Transformations ◽  
Infinite Matrices ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Convergent Sequences

Characterized are matrix transformations related to certain subsets of the space of ideal convergent sequences. Obtained here results are connected with the previous investigations of the author on some transformations defined by infinite matrices of bounded linear operators.

scholarly journals Uniform Toeplitz matrices

1990 ◽  
Vol 13 (2) ◽  
pp. 227-232 ◽  
Author(s):  
I. J. Maddox
Keyword(s):  
Banach Space ◽  
Tauberian Theorem ◽  
Toeplitz Matrices ◽  
Linear Operators ◽  
Infinite Matrices ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Uniformly Convergent ◽  
Infinite Set ◽  
Convergent Sequences

We characterize all infinite matrices of bounded linear operators on a Banach space which preserve the limits of uniformly convergent sequences defined on an infinite set. Also, we give a Tauberian theorem for uniform summability by the Kuttner-Maddox matrix.

Spaces of Ideal Convergent Sequences of Bounded Linear Operators

2018 ◽  
Vol 39 (12) ◽  
pp. 1278-1290 ◽  
Author(s):  
Vakeel A. Khan ◽  
Kamal M. A. S. Alshlool ◽  
Sameera A. A. Abdullah
Keyword(s):  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Convergent Sequences

scholarly journals Applications of Measure of Noncompactness in Matrix Operators on Some Sequence Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
M. Mursaleen ◽  
A. Latif
Keyword(s):  
Hausdorff Measure ◽  
Sequence Space ◽  
Measure Of Noncompactness ◽  
Linear Operators ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Hausdorff Measure Of Noncompactness ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Matrix Operators

We determine the conditions for some matrix transformations fromn(ϕ), where the sequence spacen(ϕ), which is related to theℓpspaces, was introduced by Sargent (1960). We also obtain estimates for the norms of the bounded linear operators 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 Some analogues of Knopp’s core theorem

1979 ◽  
Vol 2 (4) ◽  
pp. 605-614 ◽  
Author(s):  
I. J. Maddox
Keyword(s):  
Banach Space ◽  
Linear Operators ◽  
Classical Theorem ◽  
Infinite Matrices ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
The Core ◽  
Core Of A Sequence ◽  
Bounded Sequences

Inequalities between certain functionals on the space of bounded real sequences are considered. Such inequalities being analogues of the classical theorem of Knopp on the core of a sequence. Also, a result is given on infinite matrices of bounded linear operators acting on bounded sequences in a Banach space.

Matrix mappings and general bounded linear operators on the space bv

2018 ◽  
Vol 68 (2) ◽  
pp. 405-414
Author(s):  
Ivana Djolović ◽  
Katarina Petković ◽  
Eberhard Malkowsky
Keyword(s):  
Linear Operator ◽  
Bounded Linear Operator ◽  
Linear Operators ◽  
Matrix Transformations ◽  
Infinite Matrix ◽  
Hausdorff Measures ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
The Matrix ◽  
The Difference

Abstract If X and Y are FK spaces, then every infinite matrix A ∈ (X, Y) defines a bounded linear operator LA ∈ B(X, Y) where LA(x) = Ax for each x ∈ X. But the converse is not always true. Indeed, if L is a general bounded linear operator from X to Y, that is, L ∈ B(X, Y), we are interested in the representation of such an operator using some infinite matrices. In this paper we establish the representations of the general bounded linear operators from the space bv into the spaces ℓ∞, c and c0. We also prove some estimates for their Hausdorff measures of noncompactness. In this way we show the difference between general bounded linear operators between some sequence spaces and the matrix operators associated with matrix transformations.

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)$.

Cline’s formula for g-Drazin inverses in a ring

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2249-2255
Author(s):  
Huanyin Chen ◽  
Marjan Abdolyousefi
Keyword(s):  
Operator Theory ◽  
Spectral Properties ◽  
Associative Ring ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cline’S Formula

It is well known that for an associative ring R, if ab has g-Drazin inverse then ba has g-Drazin inverse. In this case, (ba)d = b((ab)d)2a. This formula is so-called Cline?s formula for g-Drazin inverse, which plays an elementary role in matrix and operator theory. In this paper, we generalize Cline?s formula to the wider case. In particular, as applications, we obtain new common spectral properties of bounded linear operators.

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