Abstract:In this paper we characterize the class of polynomially Riesz strongly continuous semigroups on a Banach space $X$. Our main results assert, in particular, that the generators of such semigroups are either polynomially Riesz (then bounded) or there exist two closed infinite dimensional invariant subspaces $X_0$ and $X_1$ of $X$ with $X=X_0\oplus X_1$ such that the part of the generator in $X_0$ is unbounded with resolvent of Riesz type while its part in $X_1$ is a polynomially Riesz operator.
Keywords: strongly continuous semigroups, Riesz operators, polynomially Riesz operators
AMS Subject Classification: 47B06, 47D03