$C_0$-semigroups and Local spectral theory
Resumen
Let $(T(t))_{t\geq0}$ be a $C_{0}$-semigroup of operators on a Banach space $X$. In this paper, we show that if there exists $t_0>0$ such that $T(t_0)$ has the SVEP then $(T(t))_{t\geq0}$ has the SVEP. Also, some local spectral properties for $C_0$ semigroups and theirs generators and some stabilities results are also established.
Descargas
Citas
P. Aiena, C. Trapani, S. Triolo, SVEP and local specral radius formula for unbounded operators, Filomat 28:2 (2014), 263-273. https://doi.org/10.2298/FIL1402263A
A. Elkoutri and M. A. Taoudi, Spectre singulier pour les generateurs des semi-groupes, C. R. Acad. Sci. Paris Ser. I Math., 333 (2001), no. 7, 641-644 (French). https://doi.org/10.1016/S0764-4442(01)02021-3
A. Elkoutri and M. A. Taoudi, Spectral Inclusions and stability results for strongly continuous semigroups, Int. J. of Math. and Mathematical Sciences, 37 (2003), 2379-2387. https://doi.org/10.1155/S0161171203202088
K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics, vol. 194, Springer-Verlag, New York, 2000.
I. Erdelyi and Wang Shengwang, A Local Spectral Theory for Closed Operators, Cambridge University Press (London-New York-New Rochelle-Melbourne-Sydney), 1985. https://doi.org/10.1017/CBO9780511662249
K. B. Laursen, M. M. Neumann. An introduction to Local Spectral Theory in: London Mathematical Society Monograph, New series, Vol. 20, Clarendon Press, Oxford, 2000
V. Muller, Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras 2nd edition. Oper. Theory Advances and Applications, vol. 139 (2007).
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York 1983. https://doi.org/10.1007/978-1-4612-5561-1
Derechos de autor 2022 Boletim da Sociedade Paranaense de Matemática
Esta obra está bajo licencia internacional Creative Commons Reconocimiento 4.0.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
