P-adic discrete semigroup of contractions

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-4413

Keywords:

Non-archimedean Banach spaces, Spectral operator, Discrete semigroup of contractions

Abstract

Let A ∈ B(X) be a spectral operator on a non-archimedean Banach space over Cp. In this paper, we give a necessary and sufficient condition on the resolvent of A so that the discrete semigroup consisting of powers of A is contractions.

Author Biographies

Abdelkhalek El amrani, Sidi Mohamed Ben Abdellah University.

Department of mathematics and computer science, Faculty of Sciences Dhar El Mahraz.

Jawad Ettayb, Sidi Mohamed Ben Abdellah University.

Department of mathematics and computer science, Faculty of Sciences Dhar El Mahraz.

Aziz Blali, Sidi Mohamed Ben Abdellah University.

Department of Mathematics. Ecole Normale Supérieure.

References

A. El Amrani, A. Blali, J. Ettayb, and M. Babahmed, “A note on C0-groups and C-groups on non-archimedean Banach spaces”, Asian-European journal of mathematics, vol. 14, no. 06, Art. ID. 2150104, 2020.

A. G. Gibson, “A discrete Hille-Yoshida-Phillips theorem”, Journal of mathematical analysis and applications, vol. 39, pp. 761-770, 1972.

N. Koblitz, P-adic analysis: A short course on recent work. Cambridge: Cambridge University Press, 1980.

A. C. M. van Rooij, Non-Archimedean functional analysis. New York, NY: Dekker, 1978.

W. H. Schikhof, “On p-adic compact operators”, Catholic University, Department of Mathematics, Nijmegen, The Netherlands, Tech. Rep. 8911, 1989.

A. Pazy, Semigroups of linear operators and applications to partial differential equations. New York, NY: Springer, 1983.

Published

2021-11-29

How to Cite

[1]
A. El amrani, J. Ettayb, and A. Blali, “P-adic discrete semigroup of contractions”, Proyecciones (Antofagasta, On line), vol. 40, no. 6, pp. 1507-1519, Nov. 2021.

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