A Hille-Yosida-Phillips theorem for discrete semigroups on complete ultrametric locally convex spaces. (English) Zbl 07777293
Summary: 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.
MSC:
47Dxx | Groups and semigroups of linear operators, their generalizations and applications |
46Sxx | Other (nonclassical) types of functional analysis |
47Sxx | Other (nonclassical) types of operator theory |
References:
[1] | Blali, A.; Amrani, A. El; Ettayb, J., A note on discrete semigroups of bounded linear operators on non-archimedean Banach spaces, Commun. Korean Math. Soc., 37, 2, 409-414 (2022) · Zbl 07523390 |
[2] | Amrani, A. El; Blali, A.; Ettayb, J.; Babahmed, M., A note on \(C_0\)-groups and \(C\)-groups on non-archimedean Banach spaces, Asian Europ. J. Math., 0 (2020) · Zbl 07374082 |
[3] | Amrani, A. El; Ettayb, J.; Blali, A., \(p\)-Adic discrete semigroup of contractions, Proyecciones (Antofagasta), 40, 6, 1507-1519 (2021) · Zbl 1491.47082 · doi:10.22199/issn.0717-6279-4413 |
[4] | Amrani, A. El; Ettayb, J.; Blali, A., \(C\)-groups and mixed \(C\)-groups of bounded linear operators on non-archimedean Banach spaces, Rev. Un. Mat. Argentina, 63, 1, 185-201 (2022) · Zbl 07581611 · doi:10.33044/revuma.2074 |
[5] | Ettayb, J., Further results on -adic semigroup of contractions (2022) |
[6] | Gibson, A. G., A discrete Hille-Yosida-Phillips theorem, J. Math. Anal. Appl., 39, 761-770 (1972) · Zbl 0213.14504 · doi:10.1016/0022-247X(72)90196-5 |
[7] | Monna, A. F., Analyse non-archimédienne (1970), New York: Springer-Verlag, New York · Zbl 0203.11501 · doi:10.1007/978-3-662-00231-5 |
[8] | Mukherjee, R. N., A Hille-Yosida-Phillips type of theorem for semi-groups in locally convex space, Indian J. Pure Appl. Math., 9, 8, 718-721 (1978) · Zbl 0405.47025 |
[9] | Garcia, C. Perez; Schikhof, W. H., Locally Convex Spaces over non-Archimedean Valued Fields (2010), Cambridge Univ. Press · Zbl 1193.46001 · doi:10.1017/CBO9780511729959 |
[10] | W. H. Schikhof, “On \(p\)-adic compact operators,” Tech. Report 8911, Departement of Mathematics, Catholic University, Nijmengen, The Netherlands, 1-28 (1989). |
[11] | Vishik, M., Non-archimedean spectral theory, J. Sov. Math., 30, 2513-2554 (1985) · Zbl 0571.46052 · doi:10.1007/BF02249122 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.