Cosine families in GDP Quojection-Fréchet spaces
Résumé
We prove that if the Quojection-Fréchet space $X$ is a Grothendieck space with the Dunford-Pettis property, then every $C_ {0}$-cosine family is necessarily uniformly continuous and therefore its infinitesimal generator is a continuous linear operator.
Téléchargements
Références
A. A. Albanese, J. Bonet, W. J. Ricker, Grothendieck spaces with the Dunford-Pettis property, positivity 14, (2010), 145-164. https://doi.org/10.1007/s11117-009-0011-x
A. A. Albanese, J. Bonet, W. J. Ricker, C0-semigroups and mean ergodic operators in a class of Frechet spaces, J. Math. Anal. Appl. 365, (2010), 142-157.
R. Ameziane, A. Blali, A. Elamrani, K. Moussaouja, Cosine families of operators in a class of Frechet spaces, Proy. J. Math. 37, (2018), 103-118. https://doi.org/10.4067/S0716-09172018000100103
W. Arendt, C. J. K. Batty, M. Hieber, F. Neubrander, Vector-valued Laplace transforms and Cauchy problems, Birkhauser, Basel, (2001). https://doi.org/10.1007/978-3-0348-5075-9
S. F. Bellenot, E. Dudinsky, Frechet spaces with nuklear Kothe. Trans. Amer. Math. Soc. 237, (1982), 579-594. https://doi.org/10.2307/1999929
J. A. Conejero, On the existence of transitive and topologically mixing semigrous. Bull. Bely. Math. soc. Simon stevin 14, (2007), 463-471. https://doi.org/10.36045/bbms/1190994207
S. Dierolf, D. N. Zarnadze, A note on strictly regular Frechet spaces, Arch. Math. 42, (1984), 549-556. https://doi.org/10.1007/BF01194053
L. Dieter, Strongly continuous operator cosine functions, Functional analysis (Dubrovnik, 1981) Lecture Notes in Math., vol. 948, Springer, Berlin-New York, (1982), 73-97. https://doi.org/10.1007/BFb0069842
R. Edwards, Functional Analysis, Reinhart and Winston, New York, 1965.
H. O. Fattorini, Second order linear differential equations in Banach spaces, Elsevier Science Publishers B.V, Amsterdam, (1969). https://doi.org/10.1016/0022-0396(69)90105-3
L. Frerick, E. Jorda, T. Kalmes, J. Wengenroth, Strongly continuous semigroups on some Fr'echet spaces, J. Math. Ana. Appl. 412, (2014), 121-124. https://doi.org/10.1016/j.jmaa.2013.10.053
M. Sova, Cosine operator functions. Rozprawy Mat. 49, (1966), 1-47.
K. Yosida, Function analysis, Springer-Verlag, Berlin, (1980).
Copyright (c) 2022 Boletim da Sociedade Paranaense de Matemática
Ce travail est disponible sous la licence Creative Commons Attribution 4.0 International .
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).
