Sums of commuting operators with maximal regularity

Christian Le Merdy; Arnaud Simard

Studia Mathematica, Tome 147 (2001), p. 103-118 / Harvested from The Polish Digital Mathematics Library

Résumé

Let Y be a Banach space and let $S \subset L_{p}$ 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 be their natural extensions to $S (Y) \subset L_{p} (Y)$ . We investigate conditions that imply that ℬ + 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 $e^{- t B}$ is a positive contraction on $L_{p}$ for any t ≥ 0.

Publié le : 2001-01-01

Zbl 0996.47050

EUDML-ID : urn:eudml:doc:284922

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Christian Le Merdy; Arnaud Simard. Sums of commuting operators with maximal regularity. Studia Mathematica, Tome 147 (2001) pp. 103-118. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-2-1/