Hankel Operators Defined Between Köthe Spaces

This paper is about the operators defined between Köthe spaces whose associated matrix is a Hankel matrix. After demonstrating how these operators are defined, the conditions for continuity and compactness of these operators are constructed. It is shown that the backward and forward shift operators are mean ergodic and Cesàro bounded by establishing a relationship between the backward and forward shift operators and Hankel and Toeplitz operators on power series spaces.