scholarly journals Linear operators preserving adjoint matrix between matrix spaces

2003 ◽  
Vol 372 ◽  
pp. 287-293 ◽  
Author(s):  
Xiao Min Tang
Keyword(s):  
Linear Operators ◽  
Adjoint Matrix ◽  
Matrix Spaces

scholarly journals ON THE OSCILLATION OF SELF-ADJOINT MATRIX HAMILTONIAN SYSTEMS

2003 ◽  
Vol 46 (3) ◽  
pp. 609-625 ◽  
Author(s):  
Qigui Yang ◽  
Sui Sun Cheng
Keyword(s):  
Hamiltonian Systems ◽  
Subject Classification ◽  
Hamiltonian Matrix ◽  
Linear Functionals ◽  
Adjoint Matrix ◽  
Oscillation Criteria ◽  
Positive Linear Functionals ◽  
Matrix Spaces

AbstractBy means of monotone functionals and positive linear functionals defined on suitable matrix spaces as well as new generalized Riccati transformations, oscillation criteria for self-adjoint linear Hamiltonian matrix systems are obtained. Our results are generalizations and improvements of many existing results.AMS 2000 Mathematics subject classification: Primary 34A30; 34C10

scholarly journals Linear Maps that Preserve Any Two Term Ranks on Matrix Spaces over Anti-Negative Semirings

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 41
Author(s):  
Kyung Tae Kang ◽  
Seok-Zun Song ◽  
Young Bae Jun
Keyword(s):  
Linear Operators ◽  
Linear Map ◽  
Linear Maps ◽  
Term Rank ◽  
Q Matrix ◽  
Matrix Spaces

There are many characterizations of linear operators from various matrix spaces into themselves which preserve term rank. In this research, we characterize the linear maps which preserve any two term ranks between different matrix spaces over anti-negative semirings, which extends the previous results on characterizations of linear operators from some matrix spaces into themselves. That is, a linear map T from p × q matrix spaces into m × n matrix spaces preserves any two term ranks if and only if T preserves all term ranks if and only if T is a ( P , Q , B )-block map.

scholarly journals Linear k-power Preservers on Tensor Products of Matrices

2020 ◽  
Vol 12 (6) ◽  
pp. 110
Author(s):  
Le Yan ◽  
Yang Zhang
Keyword(s):  
Tensor Products ◽  
Linear Operators ◽  
General Matrix ◽  
Linear Map ◽  
Preserver Problems ◽  
Matrix Spaces ◽  
Products Of Matrices

Invariants and the study of the map preserving a certain invariant play vital roles in the study of the theoretical mathematics. The preserver problems are the researches on linear operators that preserve certain invariants between matrix sets. Based on the result of linear $k$-power preservers on general matrix spaces, in terms of the advantages of matrix tensor products which is not limited by the size of matrices as well as the immense actual background, the study of the structure of the linear $k$-power preservers on tensor products of matrices is essential, which is coped with in this paper. That is to characterize a linear map $f:M_{m_{1}\cdots m_{l}}\rightarrow M_{m_{1}\cdots m_{l}}$ satisfying $f(X_{1}\otimes \cdots \otimes X_{l})^{k}=f\left( (X_{1}\otimes \cdots \otimes X_{l})^{k}\right) $ for all $X_{1}\otimes \cdots \otimes X_{l}\in M_{m_{1}\cdots m_{l}}$.

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.

On αβ-statistical convergence for sequences of fuzzy mappings and Korovkin type approximation theorem

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3749-3760 ◽  
Author(s):  
Ali Karaisa ◽  
Uğur Kadak
Keyword(s):  
Statistical Convergence ◽  
Approximation Theorem ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Bernstein Operator ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Inclusion Relations ◽  
Prior Investigation

Upon prior investigation on statistical convergence of fuzzy sequences, we study the notion of pointwise ??-statistical convergence of fuzzy mappings of order ?. Also, we establish the concept of strongly ??-summable sequences of fuzzy mappings and investigate some inclusion relations. Further, we get an analogue of Korovkin-type approximation theorem for fuzzy positive linear operators with respect to ??-statistical convergence. Lastly, we apply fuzzy Bernstein operator to construct an example in support of our result.

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.

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

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