Triple reverse order law of Drazin invertible operators

In this paper we study the triple reverse-order law (ABC)D = CDBDAD for the Drazin invertible operators A,B and C under the commutative relations [AB, B] = 0, [BC, B] = 0 and [AB, BC] = 0.

Reverse order law for reflexive generalized inverses of products of matrices

10.1016/s0024-3795(97)10068-4 ◽

1998 ◽

Vol 277 (1-3) ◽

pp. 299-311 ◽

Cited By ~ 24

Author(s):

Alvaro R. De Pierro ◽

Musheng Wei

Keyword(s):

Generalized Inverses ◽

Reverse Order ◽

Reverse Order Law ◽

Products Of Matrices

The reverse order law for the Drazin inverses of multiple matrix products

10.1016/s0024-3795(01)00607-3 ◽

2002 ◽

Vol 348 (1-3) ◽

pp. 265-272 ◽

Cited By ~ 7

Author(s):

Guorong Wang

Keyword(s):

Reverse Order ◽

Reverse Order Law ◽

Matrix Products

Further results on the reverse order law for the Core inverse in C*-algebras

International Journal of Mathematics Trends and Technology ◽

10.14445/22315373/ijmtt-v67i8p506 ◽

2021 ◽

Vol 67 (8) ◽

pp. 50-60

Author(s):

Krishnaswamy D ◽

Vijayaselvi V

Keyword(s):

Reverse Order ◽

C Algebras ◽

The Core ◽

Reverse Order Law ◽

Core Inverse

Further results on the reverse order law for the Moore–Penrose inverse in rings with involution

Applied Mathematics and Computation ◽

10.1016/j.amc.2011.06.040 ◽

2011 ◽

Vol 218 (4) ◽

pp. 1478-1483 ◽

Cited By ~ 3

Author(s):

Dijana Mosić ◽

Dragan S. Djordjević

Keyword(s):

Reverse Order ◽

Reverse Order Law ◽

Rings With Involution

Generalizations of the reverse order law with related results

10.1016/0024-3795(74)90061-5 ◽

1974 ◽

Vol 8 (4) ◽

pp. 345-349 ◽

Cited By ~ 5

Author(s):

David T. Barwick ◽

Jimmie D. Gilbert

Keyword(s):

Reverse Order ◽

Mixed-type reverse order law and its equivalents

Studia Mathematica ◽

10.4064/sm204-2-2 ◽

2011 ◽

Vol 204 (2) ◽

pp. 123-136 ◽

Cited By ~ 1

Author(s):

Nebojša Č. Dinčić ◽

Dragan S. Djordjević ◽

Dijana Mosić

Keyword(s):

Mixed Type ◽

Reverse Order ◽

The reverse order law revisited

10.1016/0024-3795(86)90226-0 ◽

1986 ◽

Vol 76 ◽

pp. 241-246 ◽

Cited By ~ 49

Author(s):

R.E. Hartwig

Keyword(s):

Reverse Order ◽

A comment on some recent results concerning the reverse order law for {1,3,4}-inverses

Applied Mathematics and Computation ◽

10.1016/j.amc.2010.05.013 ◽

2010 ◽

Vol 217 (1) ◽

pp. 105-109 ◽

Cited By ~ 4

Author(s):

Dragana S. Cvetković-Ilić ◽

Vladimir Pavlović

Keyword(s):

Reverse Order ◽

Applications of completions of operator matrices to reverse order law for {1}-inverses of operators on Hilbert spaces

10.1016/j.laa.2015.06.015 ◽

2015 ◽

Vol 484 ◽

pp. 219-236 ◽

Cited By ~ 4

Author(s):

V. Pavlović ◽

D.S. Cvetković-Ilić

Keyword(s):

Hilbert Spaces ◽

Reverse Order ◽

Operator Matrices ◽

On the group invertibility of operators

Electronic Journal of Linear Algebra ◽

10.13001/1081-3810.1967 ◽

2016 ◽

Vol 31 ◽

pp. 492-510

Author(s):

Chunyuan Deng

Keyword(s):

Hilbert Spaces ◽

Main Topic ◽

Reverse Order ◽

Operator Matrices ◽

Reverse Order Law ◽

Block Operator ◽

Block Operator Matrices ◽

Group Inverses ◽

Triangular Block ◽

Equivalent Conditions

The main topic of this paper is the group invertibility of operators in Hilbert spaces. Conditions for the existence of the group inverses of products of two operators and the group invertibility of anti-triangular block operator matrices are studied. The equivalent conditions related to the reverse order law for the group inverses of operators are obtained.