Drazin spectrum of operator matrices on the Banach space Original Research Article

When Aset membership, variantB(X) and Bset membership, variantB(Y) are given, we denote by MC the operator acting on the Banach space Xcircled plusY of the form image. In this paper, it is concluded and proved that for a given pair (A,B) of operators, σD(A)union or logical sumσD(B)=σD(MC)union or logical sumW holds for every Cset membership, variantB(Y,X), where W is the union of certain holes in σD(MC), which happen to be subsets of σD(A)∩σD(B). Moreover, the set intersection operatorCset membership, variantB(Y,X)σD(MC) is investigated and an example for it is considered.