Sums of commuting operators with maximal regularity

• Autorzy: Christian Le Merdy , Arnaud Simard
• Języki publikacji: EN

Abstrakty

EN

Let Y be a Banach space and let $S ⊂ L_{p}$ be a subspace of an $L_{p}$ space, for some p ∈ (1,∞). We consider two operators B and C acting on S and Y respectively and satisfying the so-called maximal regularity property. Let ℬ and 𝓒 be their natural extensions to $S(Y) ⊂ L_{p}(Y)$. We investigate conditions that imply that ℬ + 𝓒 is closed and has the maximal regularity property. Extending theorems of Lamberton and Weis, we show in particular that this holds if Y is a UMD Banach lattice and $e^{-tB}$ is a positive contraction on $L_{p}$ for any t ≥ 0.

Kategorie tematyczne

• 47D06: One-parameter semigroups and linear evolution equations
• 46M05: Tensor products
• 47A60: Functional calculus

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 147
• Numer: 2
• Strony: 103-118

Daty

wydano

2001

Twórcy

autor

Christian Le Merdy

• Département de Mathématiques, Université de Franche-Comté, 25030 Besançon Cedex, France

autor

Arnaud Simard

• Département de Mathématiques, Université de Franche-Comté, 25030 Besançon Cedex, France

Identyfikatory

DOI

10.4064/sm147-2-1