## Drazin inverses in certain Banach algebras

## Lisa Oberbroeckling

### Department of Mathematical Sciences

Loyola College in
Maryland

Abstract:
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.