On bi-continuous cosine families

Abstract

In this article, we introduce and investigate bi-continuous cosine families. Those are inspired by the theory of bi-continuous semigroups which had an impact in the area of evolution equations in the last decades. The idea here is again that we equip the underlying Banach space with an additional locally convex topology. We will analyze both the general behavior as well as generators and resolvents of bi-continuous cosine families.

Mathematics Subject Classification (2020):

• 47D09
• 47D06
• 46A70

Key words:

• Cosine families
• non-strongly continuous cosine families
• bi-continuous semi-groups