Matrix Representation of Linear Operators

2021 ◽  
pp. 13-27
Author(s):  
Lukong Cornelius Fai
Keyword(s):  
Matrix Representation ◽  
Linear Operators

scholarly journals The weighted g-Drazin inverse for operators

2007 ◽  
Vol 82 (2) ◽  
pp. 163-181 ◽  
Author(s):  
A. Dajić ◽  
J. J. Koliha
Keyword(s):  
Banach Spaces ◽  
Linear Algebra ◽  
Open Problem ◽  
Matrix Representation ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Operator Matrix ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Weighted Drazin Inverse

AbstractThe paper introduces and studies the weighted g-Drazin inverse for bounded linear operators between Banach spaces, extending the concept of the weighted Drazin inverse of Rakočević and Wei (Linear Algebra Appl. 350 (2002), 25–39) and of Cline and Greville (Linear Algebra Appl. 29 (1980), 53–62). We use the Mbekhta decomposition to study the structure of an operator possessing the weighted g-Drazin inverse, give an operator matrix representation for the inverse, and study its continuity. An open problem of Rakočević and Wei is solved.

scholarly journals The Weighted g-drazin inverse for operators

2006 ◽  
Vol 81 (3) ◽  
pp. 405-423 ◽  
Author(s):  
A. Dajić ◽  
J. J. Koliha
Keyword(s):  
Banach Spaces ◽  
Linear Algebra ◽  
Open Problem ◽  
Matrix Representation ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Operator Matrix ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Weighted Drazin Inverse

AbstractThe paper introduces and studies the weighted g-Drazin inverse for bounded linear operators between Banach spaces, extending the concept of the weighted Drazin inverse of Rakočević and Wei (Linear Algebra Appl. 350 (2002), 25–39) and of Cline and Greville (Linear Algebra Appl. 29(1980), 53–62). We use the Mbekhta decomposition to study the structure of an operator possessing the weighted g-Drazin inverse, give an operator matrix representation for the inverse, and study its continuity. An open problem of Rakočević and Wei is solved.

scholarly journals On linear operators for which TTD is normal

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2695-2704
Author(s):  
Ramesh Yousefi ◽  
Mansour Dana
Keyword(s):  
Matrix Representation ◽  
Normal Operator ◽  
Invertible Operator ◽  
Linear Operators ◽  
Commutativity Theorem ◽  
Normal Matrices ◽  
Basic Properties ◽  
The Matrix ◽  
Normal Operators ◽  
Drazin Invertible Operator

A Drazin invertible operator T ? B(H) is called skew D-quasi-normal operator if T* and TTD commute or equivalently TTD is normal. In this paper, firstly we give a list of conditions on an operator T; each of which is equivalent to T being skew D-quasi-normal. Furthermore, we obtain the matrix representation of these operators. We also develop some basic properties of such operators. Secondly we extend the Kaplansky theorem and the Fuglede-Putnam commutativity theorem for normal operators to skew D-quasi-normal matrices.

Approximation in statistical sense to B -continuous functions by positive linear operators

2010 ◽  
Vol 47 (3) ◽  
pp. 289-298 ◽  
Author(s):  
Fadime Dirik ◽  
Oktay Duman ◽  
Kamil Demirci
Keyword(s):  
Compact Subset ◽  
Real Line ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Classical Version ◽  
Statistical Sense

In the present work, using the concept of A -statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B -continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.

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