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:
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