Some representations for the generalized Drazin inverse of block matrices in Banach algebras (Q472673)

For an element \(a\) of a Banach algebra \({\mathcal A}\), an element \(b\) is called a generalized Drazin inverse of \(a\) if \(bab=b\), \(ab=ba\) and the element \(a-a^2b\) is quasinilpotent. If such a \(b\) exists, it is unique. The author gives explicit representations of the generalized Drazin inverse of certain block matrices.