Generalized Kato-meromorphic decomposition, generalized Drazin-meromorphic invertible operators and single-valued extension property (Q778758)

A bounded linear operator \(T\) on a Banach space \(X\) is said to be generalized Drazin-meromorphic invertible if there exists a bounded linear operator \(S\) acting on \(X\) such that \(T S = ST\), \(ST S = S\), and \(T ST-T\) is meromorphic. In this paper, the authors give several characterizations of this class of operators using the Kato-Riesz meromorphic decomposition, which is a generalization of the Kato decomposition. Also, they study bounded linear operators which can be expressed as the direct sum of a meromorphic operator and a bounded below (resp., surjective, upper (lower) semi-Fredholm, Fredholm, upper (lower) semi-Weyl, Weyl) operator.