An operator on a complex Banach space is called Drazin invertible if there exists another operator on such that , and for some nonnegative integer . The Drazin spectrum of is the set .
Given two complex Banach spaces and , the authors consider operators on the product space defined by a upper triangular matrix with and in the diagonal and in the upper right entry. They show that , where is the union of certain holes in contained in . Moreover, they study the set .