Drazin inverses in certain Banach algebras

Lisa Oberbroeckling

Department of Mathematical Sciences
Loyola College in Maryland


If a dual system of Banach spaces has a bilinear form that is also bounded, the Jörgens algebra is the Banach algebra of operators that have bounded linear adjoints with respect to the form. This algebra was discussed in a previous paper in which generalized inverses in this algebra were characterized. In this talk, we will extend these results and characterize Drazin inverses in the Jörgens algebra. Generalized and Drazin inverses in other algebras of bounded linear operators will also be discussed.