Sums of commuting operators with maximal regularity

Volume 147 / 2001

Christian Le Merdy, Arnaud Simard Studia Mathematica 147 (2001), 103-118 MSC: Primary 47D06; Secondary 47A60, 46M05. DOI: 10.4064/sm147-2-1

Abstract

Let $Y$ be a Banach space and let $S\subset L_p$ be a subspace of an $L_p$ space, for some $p\in (1,\infty )$. We consider two operators $B$ and $C$ acting on $S$ and $Y$ respectively and satisfying the so-called maximal regularity property. Let ${\cal B}$ and ${\cal C}$ be their natural extensions to $S(Y)\subset L_p(Y)$. We investigate conditions that imply that ${\cal B} +{\cal C}$ 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 $t\geq 0$.

Authors

  • Christian Le MerdyDépartement de Mathématiques
    Université de Franche-Comté
    25030 Besançon Cedex, France
    e-mail
  • Arnaud SimardDépartement de Mathématiques
    Université de Franche-Comté
    25030 Besançon Cedex, France
    e-mail

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