Continuous maximal regularity in locally convex spaces
Volume 285 / 2025
Studia Mathematica 285 (2025), 41-89
MSC: Primary 34A12; Secondary 47D06, 35K90, 46A30, 46A70
DOI: 10.4064/sm240822-31-7
Published online: 18 October 2025
Abstract
We study maximal regularity with respect to continuous functions for strongly continuous semigroups on locally convex spaces as well as its relation to the notion of admissible operators. This extends several results for classical strongly continuous semigroups on Banach spaces. In particular, we show that Travis’ characterization of $\mathrm C$-maximal regularity using the notion of bounded semivariation carries over to the general case. Under some topological assumptions, we further show the equivalence between maximal regularity and admissibility in this context.
