Left and Right Generalized Drazin Invertible Operators on Banach Spaces: New Pre-orders and Partial Orders

D.E. FERREYRA; M. LATTANZI; F.E. LEVIS; N. THOME

Villa General Belgrano, Cba.

Encuentro; XIII Encuentro de Analistas A.P. Calderón; 2016

In this work new binary relations on the set of bounded linear operatorson an infinite-dimensional Banach space are introduced and characterizedby using the left and right generalized Drazin inverses recently defined by Hocine,Benharrat, and Messirdi. A new characterization of the generalized Drazinpre-order and a sufficient condition for that to be a partial order are given.