On obtient certains théorèmes ergodiques maximaux dans les espaces Lp non commutatifs associés à une algèbre de von Neumann semifinie.
We prove several maximal ergodic theorems in non-commutative Lp-spaces associated with semifinite von Neumann algebras.
Accepté le :
Publié le :
@article{CRMATH_2002__334_9_773_0, author = {Junge, Marius and Xu, Quanhua}, title = {Th\'eor\`emes ergodiques maximaux dans les espaces $ \mathrm{L}_{\mathbf{p}}$ non commutatifs}, journal = {Comptes Rendus. Math\'ematique}, pages = {773--778}, publisher = {Elsevier}, volume = {334}, number = {9}, year = {2002}, doi = {10.1016/S1631-073X(02)02367-1}, language = {fr}, url = {http://archive.numdam.org/articles/10.1016/S1631-073X(02)02367-1/} }
TY - JOUR AU - Junge, Marius AU - Xu, Quanhua TI - Théorèmes ergodiques maximaux dans les espaces $ \mathrm{L}_{\mathbf{p}}$ non commutatifs JO - Comptes Rendus. Mathématique PY - 2002 SP - 773 EP - 778 VL - 334 IS - 9 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(02)02367-1/ DO - 10.1016/S1631-073X(02)02367-1 LA - fr ID - CRMATH_2002__334_9_773_0 ER -
%0 Journal Article %A Junge, Marius %A Xu, Quanhua %T Théorèmes ergodiques maximaux dans les espaces $ \mathrm{L}_{\mathbf{p}}$ non commutatifs %J Comptes Rendus. Mathématique %D 2002 %P 773-778 %V 334 %N 9 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(02)02367-1/ %R 10.1016/S1631-073X(02)02367-1 %G fr %F CRMATH_2002__334_9_773_0
Junge, Marius; Xu, Quanhua. Théorèmes ergodiques maximaux dans les espaces $ \mathrm{L}_{\mathbf{p}}$ non commutatifs. Comptes Rendus. Mathématique, Tome 334 (2002) no. 9, pp. 773-778. doi : 10.1016/S1631-073X(02)02367-1. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02367-1/
[1] Ultracontractivity and strong Sobolev inequality for q-Ornstein–Uhlenbeck semigroup (−1<q<1), Infinite Dimensional Anal., Quantum Probab. Related Topics, Volume 2 (1999), pp. 203-220
[2] q-Gaussian processes: Non-commutative and classical aspects, Comm. Math. Phys., Volume 185 (1997), pp. 129-154
[3] Ergodic theorems for noncommutative dynamical systems, Invent. Math., Volume 46 (1978), pp. 1-15
[4] Martingales on von Neumann algebras, J. Multivariate. Anal., Volume 1 (1971), pp. 17-27
[5] Strong Limit Theorems on Non-Commutative Probability, Lecture Notes in Math., 1110, Springer, 1985
[6] M. Junge, Doob's inequality for non-commutative martingales, J. Reine Angew. Math., to appear
[7] M. Junge, Q. Xu, The optimal orders of growth of the best constants in some non-commutative martingale inequalities, en préparation
[8] A non-commutative individual ergodic theorem, Invent. Math., Volume 46 (1978), pp. 139-145
[9] Ergodic theorems for convex sets and operator algebras, Invent. Math., Volume 37 (1976), pp. 201-214
[10] Non-commutative vector valued Lp-spaces and completely p-summing maps, Astérisque, Volume 247 (1998)
[11] On the maximal ergodic theorem, Proc. Nat. Acad. Sci., Volume 47 (1961), pp. 1894-1897
[12] Topics in harmonic analysis related to the Littlewood–Paley theory, Ann. Math. Studies, Princeton University Press, 1985
[13] Ergodic theorems for semifinite von Neumann algebras. I, J. London Math. Soc., Volume 16 (1977), pp. 326-332
Cité par Sources :