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

Abstract

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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 ⊕ 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.

How to cite

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Latrach, 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 -

References

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