Group inverse and generalized Drazin inverse of block matrices in a Banach algebra. (English) Zbl 1301.46026
Summary: Necessary and sufficient conditions for the existence of the group inverse of an anti-triangular block matrix in Banach algebras are presented. Using these results, we give formulae for the generalized Drazin inverse of a block matrix.
MSC:
| 46H05 | General theory of topological algebras |
| 47A05 | General (adjoints, conjugates, products, inverses, domains, ranges, etc.) |
| 15A09 | Theory of matrix inversion and generalized inverses |
