Loading…
Additive property of Drazin invertibility of elements in a ring
In this article, we investigate additive properties on the Drazin inverse of elements in rings. Under the commutative condition of ab = ba, we show that a + b is Drazin invertible if and only if 1 + a D b is Drazin invertible. Not only the explicit representations of the Drazin inverse (a + b) D in...
Saved in:
Published in: | Linear & multilinear algebra 2012-08, Vol.60 (8), p.903-910 |
---|---|
Main Authors: | , , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Summary: | In this article, we investigate additive properties on the Drazin inverse of elements in rings. Under the commutative condition of ab = ba, we show that a + b is Drazin invertible if and only if 1 + a
D
b is Drazin invertible. Not only the explicit representations of the Drazin inverse (a + b)
D
in terms of a, a
D
, b and b
D
, but also (1 + a
D
b)
D
is given. Further, the same property is inherited by the generalized Drazin invertibility in a Banach algebra and is extended to bounded linear operators. |
---|---|
ISSN: | 0308-1087 1563-5139 |
DOI: | 10.1080/03081087.2011.629998 |