A refinement of Baillon's theorem on maximal regularity

Abstract

By Baillon's result, it is known that maximal regularity with respect to the space of continuous functions is rare; it implies that either the involved semigroup generator is a bounded operator or the considered space contains $c_0$. We show that the latter alternative can be excluded under a refined condition resembling maximal regularity with respect to ${\mathrm{L}}^{\infty }$.

17 pages, typos corrected, several references were added