On Meromorphic Operators, I

Abstract

If X is a complex Banach space and B(X) denotes the space of bounded linear operators on X, then the class of meromorphic operators consists of those T in B(X) such that the non-zero points of σ(T) are poles of the resolvent Rλ(T). If we also require that each non-zero eigenvalue of T have finite multiplicity, members of the class ⊆ so defined have been called operators of Riesz type. and have been studied in (2, 6, 7) and (1,4) respectively.