On properties of the minus partial order in regular modules

2020 ◽  
Vol 96 (1-2) ◽  
pp. 149-159
Author(s):  
Burcu Ungor ◽  
Sait Halicioglu ◽  
Abdullah Harmanci ◽  
Janko Marovt
Keyword(s):  
Partial Order ◽  
Minus Partial Order

Inverse complements and strongly unit regular elements

2021 ◽  
pp. 2250190
Author(s):  
Umashankara Kelathaya ◽  
Savitha Varkady ◽  
Manjunatha Prasad Karantha
Keyword(s):  
Partial Order ◽  
Regular Element ◽  
Generalized Inverse ◽  
Generalized Inverses ◽  
Order Unit ◽  
Regular Elements ◽  
Strongly Regular ◽  
Minus Partial Order

In this paper, the notion of “strongly unit regular element”, for which every reflexive generalized inverse is associated with an inverse complement, is introduced. Noting that every strongly unit regular element is unit regular, some characterizations of unit regular elements are obtained in terms of inverse complements and with the help of minus partial order. Unit generalized inverses of given unit regular element are characterized as sum of reflexive generalized inverses and the generators of its annihilators. Surprisingly, it has been observed that the class of strongly regular elements and unit regular elements are the same. Also, several classes of generalized inverses are characterized in terms of inverse complements.

scholarly journals Nilpotent matrices and the minus partial order

2017 ◽  
Vol 40 (4) ◽  
pp. 519-525 ◽  
Author(s):  
M.I. Gareis ◽  
M. Lattanzi ◽  
N. Thome
Keyword(s):  
Partial Order ◽  
Nilpotent Matrices ◽  
Minus Partial Order

WEIGHTED CORE–EP INVERSE AND WEIGHTED CORE–EP PRE-ORDERS IN A -ALGEBRA

2019 ◽  
pp. 1-35 ◽  
Author(s):  
DIJANA MOSIĆ
Keyword(s):  
Partial Order ◽  
Hilbert Spaces ◽  
Partial Orders ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
The Core ◽  
Invertible Elements ◽  
Minus Partial Order

We define extensions of the weighted core–EP inverse and weighted core–EP pre-orders of bounded linear operators on Hilbert spaces to elements of a $C^{\ast }$ -algebra. Some properties of the weighted core–EP inverse and weighted core–EP pre-orders are generalized and some new ones are proved. Using the weighted element, the weighted core–EP pre-order, the minus partial order and the star partial order of certain elements, new weighted pre-orders are presented on the set of all $wg$ -Drazin invertible elements of a $C^{\ast }$ -algebra. Applying these results, we introduce and characterize new partial orders which extend the core–EP pre-order to a partial order.

scholarly journals Nonnegative idempotent matrices and the minus partial order

1997 ◽  
Vol 261 (1-3) ◽  
pp. 143-154 ◽  
Author(s):  
R.B. Bapat ◽  
S.K. Jain ◽  
L.E. Snyder
Keyword(s):  
Partial Order ◽  
Minus Partial Order

scholarly journals Minus partial order in regular modules

2020 ◽  
Vol 48 (10) ◽  
pp. 4542-4553
Author(s):  
B. Ungor ◽  
S. Halicioglu ◽  
A. Harmanci ◽  
J. Marovt
Keyword(s):  
Partial Order ◽  
Minus Partial Order

On a generalized concept of order relations on B(H)

2018 ◽  
Vol 68 (1) ◽  
pp. 33-40 ◽  
Author(s):  
Gregor Dolinar ◽  
Janko Marovt
Keyword(s):  
Hilbert Space ◽  
Partial Order ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Order Relations ◽  
The Right ◽  
Minus Partial Order

AbstractLetHbe a Hilbert space andB(H) the set of all bounded linear operators onH. In the paper we consider the generalized concept of order relations onB(H) which was proposed by Šemrl and which covers the star partial order, the left-star partial order, the right-star partial order, and the minus partial order. We also connect this concept with the sharp partial order.

Space pre-order and minus partial order for operators on Banach spaces

2012 ◽  
Vol 85 (3) ◽  
pp. 429-448 ◽  
Author(s):  
Dragan S. Rakić ◽  
Dragan S. Djordjević
Keyword(s):  
Partial Order ◽  
Banach Spaces ◽  
Minus Partial Order

scholarly journals Preservers of partial orders on the set of all variance-covariance matrices

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 617-632
Author(s):  
Iva Golubic ◽  
Janko Marovt
Keyword(s):  
Partial Order ◽  
Positive Semidefinite ◽  
Covariance Matrices ◽  
Partial Orders ◽  
Equivalent Definition ◽  
Definition Of ◽  
Square Complex ◽  
Additive Maps ◽  
Minus Partial Order ◽  
Real Matrices

Let H+n(R) be the cone of all positive semidefinite n x n real matrices. Two of the best known partial orders that were mostly studied on subsets of square complex matrices are the L?wner and the minus partial orders. Motivated by applications in statistics we study these partial orders on H+ n (R). We describe the form of all surjective maps on H+ n (R), n > 1, that preserve the L?wner partial order in both directions. We present an equivalent definition of the minus partial order on H+ n (R) and also characterize all surjective, additive maps on H+ n (R), n ? 3, that preserve the minus partial order in both directions.

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