Another special role of $ \mathrm{L}^\infty $-spaces-evolution equations and Lotz' theorem

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 $ \mathrm{L}...

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Bibliographic Details

Published in:	AIMS Mathematics
Main Author:	Christian Budde
Format:	Article
Language:	English
Published:	AIMS Press 2024-12-01
Subjects:	$ \mathrm{l}^\infty $-spaces lotz' theorem grothendieck spaces dunford-pettis property
Online Access:	https://www.aimspress.com/article/doi/10.3934/math.20241716