Abstract
Let \(E\) be a complete Hausdorff locally convex space over \(\mathbb{C}_{p},\) let \(A\in\mathcal{L}(E)\) such that \((I-\lambda A)^{-1}\) is analytic on its domain. In this paper, we give a necessary and sufficient condition on the resolvent of \(A\) such that \((A^{n})_{n\in\mathbb{N}}\) is equi-continuous.
References
A. Blali, A. El Amrani and J. Ettayb, “A note on discrete semigroups of bounded linear operators on non-archimedean Banach spaces,” Commun. Korean Math. Soc. 37 (2), 409–414 (2022).
A. El Amrani, A. Blali, J. Ettayb and M. Babahmed, “A note on \(C_{0}\)-groups and \(C\)-groups on non-archimedean Banach spaces,” Asian Europ. J. Math. 2150104 (2020).
A. El Amrani, J. Ettayb and A. Blali, “\(p\)-Adic discrete semigroup of contractions,” Proyecciones (Antofagasta) 40 (6), 1507–1519 (2021).
A. El Amrani, J. Ettayb and A. Blali, “\(C\)-groups and mixed \(C\)-groups of bounded linear operators on non-archimedean Banach spaces,” Rev. Un. Mat. Argentina 63 (1), 185–201 (2022).
J. Ettayb, “Further results on \(p\)-adic semigroup of contractions,” arXiv:2211.12630 (2022).
A. G. Gibson, “A discrete Hille-Yosida-Phillips theorem,” J. Math. Anal. Appl. 39, 761–770 (1972).
A. F. Monna, Analyse non-archimédienne (Springer-Verlag, New York, 1970).
R. N. Mukherjee, “A Hille-Yosida-Phillips type of theorem for semi-groups in locally convex space,” Indian J. Pure Appl. Math. 9 (8), (1978) 718-721.
C. Perez Garcia and W. H. Schikhof, Locally Convex Spaces over non-Archimedean Valued Fields (Cambridge Univ. Press, 2010).
W. H. Schikhof, “On \(p\)-adic compact operators,” Tech. Report 8911, Departement of Mathematics, Catholic University, Nijmengen, The Netherlands, 1–28 (1989).
M. Vishik, “Non-archimedean spectral theory,” J. Sov. Math. 30, 2513–2554 (1985).
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Ettayb, J. A Hille-Yosida-Phillips Theorem for Discrete Semigroups on Complete Ultrametric Locally Convex Spaces. P-Adic Num Ultrametr Anal Appl 15, 113–118 (2023). https://doi.org/10.1134/S2070046623020048
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DOI: https://doi.org/10.1134/S2070046623020048