The Cesàro operator on power series spaces
Tom 240 / 2018
Streszczenie
The discrete Cesàro operator is investigated in the class of power series spaces \varLambda _0(\alpha ) of finite type. Of main interest is its spectrum, which is distinctly different in the cases when \varLambda _0(\alpha ) is nuclear and when it is not. Actually, the nuclearity of \varLambda _0(\alpha ) is characterized via certain properties of the spectrum of \mathsf {C}. Moreover, \mathsf {C} is always power bounded, uniformly mean ergodic, and whenever \varLambda _0(\alpha ) is nuclear, also (I-\mathsf {C})^m(\varLambda _0(\alpha )) is closed in \varLambda _0(\alpha ) for each m\in {\mathbb N}.