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- Title
Some Results on the Symmetric Representation of the Generalized Drazin Inverse in a Banach Algebra.
- Authors
Qin, Yonghui; Liu, Xiaoji; Benítez, Julio
- Abstract
Based on the conditions a b 2 = 0 and b π (a b) ∈ A d , we derive that (a b) n , (b a) n , and a b + b a are all generalized Drazin invertible in a Banach algebra A , where n ∈ N and a and b are elements of A. By using these results, some results on the symmetry representations for the generalized Drazin inverse of a b + b a are given. We also consider that additive properties for the generalized Drazin inverse of the sum a + b .
- Subjects
MATHEMATICAL symmetry; GENERALIZATION; INVERSE problems; BANACH algebras; BANACH spaces
- Publication
Symmetry (20738994), 2019, Vol 11, Issue 1, p105
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym11010105