New additive results for the Drazin inverse of multivalued operators.

The concept of the Drazin inverse of multivalued operators in a Banach space studied by A. Ghorbel and M. Mnif [Monatsh Math. 2019;189:273–293] is generalized in the context of the generalized Drazin inverse of multivalued operators [Rocky Mountain J Math. 2020;50(4):1387–1408]. The purpose of this paper is to present new additive results for this concept. In particular, we give a sufficient condition for an everywhere defined linear relation to have at most one Drazin inverse. Some properties and the explicit expressions for the Drazin inverse of the product are obtained. Also, some results of C. Deng, H. Du [Proc Amer Math Soc. 2006;134:3309–3317] concerning the reduced minimum modulus of Drazin inverses of linear operators on Hilbert spaces are extended to the case of linear relations. [ABSTRACT FROM AUTHOR]