On introduit des fonctions carrées adaptées à l'étude des opérateurs sectoriels sur les espaces Lp non commutatifs, et on étudie leurs relations avec le calcul fonctionnel H∞.
We introduce suitable square functions for sectorial operators on noncommutative Lp-spaces, and we investigate their relationships with H∞ functional calculus.
Accepté le :
Publié le :
Junge, Marius 1 ; Le Merdy, Christian 2 ; Xu, Quanhua 2
@article{CRMATH_2003__337_2_93_0,
author = {Junge, Marius and Le Merdy, Christian and Xu, Quanhua},
title = {Calcul fonctionnel et fonctions carr\'ees dans les espaces {\protect\emph{L}\protect\textsuperscript{\protect\emph{p}}} non commutatifs},
journal = {Comptes Rendus. Math\'ematique},
pages = {93--98},
year = {2003},
publisher = {Elsevier},
volume = {337},
number = {2},
doi = {10.1016/S1631-073X(03)00276-0},
language = {fr},
url = {https://www.numdam.org/articles/10.1016/S1631-073X(03)00276-0/}
}
TY - JOUR AU - Junge, Marius AU - Le Merdy, Christian AU - Xu, Quanhua TI - Calcul fonctionnel et fonctions carrées dans les espaces Lp non commutatifs JO - Comptes Rendus. Mathématique PY - 2003 SP - 93 EP - 98 VL - 337 IS - 2 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/S1631-073X(03)00276-0/ DO - 10.1016/S1631-073X(03)00276-0 LA - fr ID - CRMATH_2003__337_2_93_0 ER -
%0 Journal Article %A Junge, Marius %A Le Merdy, Christian %A Xu, Quanhua %T Calcul fonctionnel et fonctions carrées dans les espaces Lp non commutatifs %J Comptes Rendus. Mathématique %D 2003 %P 93-98 %V 337 %N 2 %I Elsevier %U https://www.numdam.org/articles/10.1016/S1631-073X(03)00276-0/ %R 10.1016/S1631-073X(03)00276-0 %G fr %F CRMATH_2003__337_2_93_0
Junge, Marius; Le Merdy, Christian; Xu, Quanhua. Calcul fonctionnel et fonctions carrées dans les espaces Lp non commutatifs. Comptes Rendus. Mathématique, Tome 337 (2003) no. 2, pp. 93-98. doi: 10.1016/S1631-073X(03)00276-0
[1] q-Gaussian processes: non-commutative and classical aspects, Comm. Math. Phys., Volume 185 (1997), pp. 129-154
[2] Harmonic analysis on semigroups, Ann. of Math., Volume 117 (1983), pp. 267-283
[3] Banach space operators with a bounded H∞ functional calculus, J. Austral. Math. Soc. Ser. A, Volume 60 (1996), pp. 51-89
[4] Semigroups of Linear Operators and Applications, Oxford University Press, New York, NY, 1985
[5] Théorèmes ergodiques maximaux dans les espaces Lp non commutatifs, C. R. Acad. Sci. Paris, Ser., Volume 334 (2002), pp. 773-778
[6] The H∞ calculus and sums of closed operators, Math. Ann., Volume 321 (2001), pp. 319-345
[7] C. Le Merdy, On square functions associated to sectorial operators, Bull. Soc. Math. France, à paraitre
[8] Inégalités de Khintchine dans Cp, C. R. Acad. Sci. Paris, Volume 303 (1986), pp. 289-292
[9] Operators which have an H∞ functional calculus, in: Miniconference on Operator Theory and Partial Differential Equations (Proc. CMA (Canberra)), Volume 14 (1986), pp. 210-231
[10] Operators of type ω without a bounded H∞ functional calculus, in: Miniconference on Operators in Analysis (Proc. CMA (Canberra)), Volume 24 (1989), pp. 159-172
[11] Non-Commutative Vector Valued Lp-Spaces and Completely p-Summing Maps, Astérisque, 247, Soc. Math. France, 1998
[12] Non-commutative martingale inequalities, Comm. Math. Phys., Volume 189 (1997), pp. 667-698
[13] Non-commutative Lp-spaces (Johnson, W.B.; Lindenstrauss, J., eds.), Handbook of the Geometry of Banach Spaces, Elsevier, 2003
[14] Topics in Harmonic Analysis Related to the Littlewood–Paley Theory, Ann. Math. Stud., Princeton University Press, 1985
[15] Operator valued Fourier multiplier theorems and maximal regularity, Math. Ann., Volume 319 (2001), pp. 735-758
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