A refinement of Baillon’s theorem on maximal regularity
Copyright policy )A refinement of Baillon’s theorem on maximal regularity
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
- Universität Hamburg Germany
- University of Wuppertal Germany
- University of Twente Netherlands
Abstract parabolic equations, One-parameter semigroups and linear evolution equations, maximal regularity, Baillon's theorem, Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.), Functional Analysis (math.FA), 47D06, 35K90, 47B37, Mathematics - Functional Analysis, strongly continuous semigroup, Mathematics - Analysis of PDEs, uniformly continuous semigroup, FOS: Mathematics, Maximal regularity, admissible operator, Analysis of PDEs (math.AP)
Abstract parabolic equations, One-parameter semigroups and linear evolution equations, maximal regularity, Baillon's theorem, Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.), Functional Analysis (math.FA), 47D06, 35K90, 47B37, Mathematics - Functional Analysis, strongly continuous semigroup, Mathematics - Analysis of PDEs, uniformly continuous semigroup, FOS: Mathematics, Maximal regularity, admissible operator, Analysis of PDEs (math.AP)
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