Geodesic
A characterization of polynomially Riesz strongly continuous semigroups
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 2, pp. 275-289.

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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.
Classification : 47B06, 47D03, 47D06
Keywords: strongly continuous semigroups; Riesz operators; polynomially Riesz operators 
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Latrach, Khalid; Paoli, J. Martin; Taoudi, M. A. A characterization of polynomially Riesz strongly continuous semigroups. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 2, pp. 275-289. http://geodesic.mathdoc.fr/item/CMUC_2006__47_2_a6/