Algebraic Operators on Banach Spaces

Abstract: In this paper, we investigate the relationship between the class of all algebraic operators, defined on a infinite-dimensional complex Banach space X , and the classes Ω+( X ) and Ω−( X ), introduced by the author in Mathematische Zeitschrift 196 and Mathematische Zeitschrift 201 , respectively. Furthermore, the operators K for which a power K n is finite dimensional are characterised among algebraic operators.