Functional Representation Theorem for Polynomially Bounded Operators on a Banach Space
一般多项式有界算子的泛函表示定理

In this paper, the author introduces a transformation by scalar multiplication of the independent variable in the disc algebra, finds the connection between the Riesz functional calculus of polynomially bounded operators and the polynomial calculus of polynomially bounded operators, and obtains the functional representation theorem for (general) polynomially bounded operators on a Banach space.