Sums of commuting operators with maximal regularity

Christian Le Merdy, and Arnaud Simard. "Sums of commuting operators with maximal regularity." Studia Mathematica 147.2 (2001): 103-118. <http://eudml.org/doc/284922>.

@article{ChristianLeMerdy2001,
abstract = {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 be their natural extensions to $S(Y) ⊂ L_\{p\}(Y)$. 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 $e^\{-tB\}$ is a positive contraction on $L_\{p\}$ for any t ≥ 0.},
author = {Christian Le Merdy, Arnaud Simard},
journal = {Studia Mathematica},
keywords = {generators; commuting bounded analytic semigroups; maximal regularity},
language = {eng},
number = {2},
pages = {103-118},
title = {Sums of commuting operators with maximal regularity},
url = {http://eudml.org/doc/284922},
volume = {147},
year = {2001},
}

TY - JOUR
AU - Christian Le Merdy
AU - Arnaud Simard
TI - Sums of commuting operators with maximal regularity
JO - Studia Mathematica
PY - 2001
VL - 147
IS - 2
SP - 103
EP - 118
AB - 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 be their natural extensions to $S(Y) ⊂ L_{p}(Y)$. 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 $e^{-tB}$ is a positive contraction on $L_{p}$ for any t ≥ 0.
LA - eng
KW - generators; commuting bounded analytic semigroups; maximal regularity
UR - http://eudml.org/doc/284922
ER -