Sums of commuting operators with maximal regularity
Volume 147 / 2001
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 $t\geq 0$.
