@article{Budde2024, 
author = {Christian Budde},
title = {Another special role of  L∞-spaces-evolution equations and Lotz' theorem},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {12},
pages = {36158-36166},
keywords = {L∞-spaces, Lotz' theorem, Grothendieck spaces, Dunford-Pettis property},
url = {https://www.sciopen.com/article/10.3934/math.20241716},
doi = {10.3934/math.20241716},
abstract = {In this paper, we review the underappreciated theorem by Lotz that tells us that every strongly continuous operator semigroup on a Grothendieck space with the Dunford-Pettis property is automatically uniformly continuous. A large class of spaces that carry these geometric properties are  L∞(Ω,Σ,μ) for non-negative measure spaces. This shows once again that  L∞-spaces have to be treated differently.}
}