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Positive Desch-Schappacher perturbations of bi-continuous semigroups on AM-spaces

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Abstract

In this paper, we consider positive Desch-Schappacher perturbations of bi-continuous semigroups on AM-spaces with an additional property concerning the additional locally convex topology. As an example, we discuss perturbations of the left-translation semigroup on the space of bounded continuous functions on the real line and on the space of bounded linear operators.

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Acknowledgment

The author is indepted to Bálint Farkas and Sanne ter Horst for the fruitful discussions, the continuous support during writing and the helpful feedback. This study was funded by the DAAD-TKA Project 308019 “Coupled systems and innovative time integrators”. Moreover, the author acknowledges fundingby the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) -468736785. The author also wants to thank the anonymous referee for the detailed feedback which helped to improve the article as a whole.

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  1. School of Mathematical and Statistical Sciences, North-West University, Private Bag X6001-209, Potchefstroom 2520, South Africa

    Christian Budde

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Communicated by L. Molnár

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Budde, C. Positive Desch-Schappacher perturbations of bi-continuous semigroups on AM-spaces. ActaSci.Math. 87, 571–594 (2021). https://doi.org/10.14232/actasm-021-914-5

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