Khalid Latrach, J. Martin Paoli, M.A. Taoudi
A characterization of polynomially Riesz strongly continuous semigroups

Comment.Math.Univ.Carolin. 47,2 (2006) 275-289.

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

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