Left and right generalized Drazin–Riesz invertible multivalued linear operators

In this paper the notions of left and right generalized Drazin–Riesz invertible linear relations are introduced and studied. For these classes of linear relations we give several characterizations which covered the ones proved in Zivkovic-Zlatanovic and Cvetkovic (Linear Multilinear Algebra 65(6):1171–1193, 2017) in the particular case of bounded operators. Some characterizations are essentially expressed by means of a Kato–Riesz decomposition and an associated projection. Among other things, we show that these linear relations are completely characterized in terms of an algebraic decomposition with a semi-Browder linear relation and a bounded Riesz operator. Finally, the application of some obtained results is given.