Generalized Drazin-Riesz invertible multivalued linear operators
Teresa Álvarez, Melik Lajnef · Linear and Multilinear Algebra · 2025
This paper initiates a study of generalized Drazin-Riesz invertible linear relations. We aim to generalize some well-known characterizations in the frame of bounded operators. First, we show that this class can be characterized in terms of an algebraic decomposition with a bounded Riesz operator and a Browder linear relation. Characterization of this class in terms of an associated projection is also given. Second, we study the interrelation between this class and an isolated point of its Browder spectrum. After that, we applied these findings to investigate the interconnection between this class and the classes of left and right generalized Drazin-Riesz invertible linear relations. As an application, we investigate the generalized Drazin-Riesz invertibility of multivalued operator matrices.