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.