# A characterization of polynomially Riesz strongly continuous semigroups

Khalid Latrach; Martin J. Paoli; Mohamed Aziz Taoudi

Commentationes Mathematicae Universitatis Carolinae (2006)

- Volume: 47, Issue: 2, page 275-289
- ISSN: 0010-2628

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topLatrach, Khalid, Paoli, Martin J., and Taoudi, Mohamed Aziz. "A characterization of polynomially Riesz strongly continuous semigroups." Commentationes Mathematicae Universitatis Carolinae 47.2 (2006): 275-289. <http://eudml.org/doc/249886>.

@article{Latrach2006,

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.},

author = {Latrach, Khalid, Paoli, Martin J., Taoudi, Mohamed Aziz},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {strongly continuous semigroups; Riesz operators; polynomially Riesz operators; strongly continuous semigroups; Riesz operators},

language = {eng},

number = {2},

pages = {275-289},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {A characterization of polynomially Riesz strongly continuous semigroups},

url = {http://eudml.org/doc/249886},

volume = {47},

year = {2006},

}

TY - JOUR

AU - Latrach, Khalid

AU - Paoli, Martin J.

AU - Taoudi, Mohamed Aziz

TI - A characterization of polynomially Riesz strongly continuous semigroups

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2006

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 47

IS - 2

SP - 275

EP - 289

AB - 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.

LA - eng

KW - strongly continuous semigroups; Riesz operators; polynomially Riesz operators; strongly continuous semigroups; Riesz operators

UR - http://eudml.org/doc/249886

ER -

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