Drazin invertibility of products

If a and b are elements of an algebra, then we show that ab is Drazin invertible if and only if ba is Drazin invertible. With this result we investigate products of bounded linear operators on Banach spaces

Relatively Regular Operators and a Spectral Mapping Theorem

AbstractLet T be a bounded linear operator on a complex banach space X. The following essential spectrum of T is introduced: [formula] In this note, for a funciton f admissable in the analytic calculus, we show that σrr(f(T)) = f(σrr(T))