Solid extensions of the Cesàro operator on the Hardy space

We introduce and study the largest Banach space of analytic functions on the unit disc which is solid for the coefficient-wise order and to which the classical Cesàro operator C : H 2 → H 2 can be continuously extended, while still maintaining its values in H 2 . Properties of this Banach space H ( c e s 2 ) as well as a characterization of individual analytic functions which belong to H ( c e s 2 ) are presented. In addition, both the multiplier space of H ( c e s 2 ) and the spectrum of C : H ( c e s 2 ) → H ( c e s 2 ) are determined.