Commutators associated to a subfactor and its relative commutants  [ Commutateurs associés à un sous-facteur et à ses commutants relatifs ]
Annales de l'Institut Fourier, Tome 52 (2002) no. 1, p. 289-301
Soit $N\subseteq M$ une inclusion de facteurs de type $I{I}_{1}$ayant un indice de Jones fini. Alors on a l’égalité $M=\left({N}^{\text{'}}\cap M\right)\oplus \left[N,M\right]$ en tant qu’espaces vectoriels. Ici $\left[N,M\right]$ désigne l’espace vectoriel engendré par les commutateurs de la forme $\left[a,b\right]$$a\in N,\phantom{\rule{0.166667em}{0ex}}b\in M$.
Let $N\subseteq M$ be an inclusion of $I{I}_{1}$ factors with finite Jones index. Then $M=\left({N}^{\text{'}}\cap M\right)\oplus \left[N,M\right]$ as a vector space. Here $\left[N,M\right]$ denotes the vector space spanned by the commutators of the form $\left[a,b\right]$ where $a\in N,\phantom{\rule{0.166667em}{0ex}}b\in M$.
DOI : https://doi.org/10.5802/aif.1887
Classification:  46L37,  47B47
Mots clés: commutateur, attente conditionnelle, commutant relatif
@article{AIF_2002__52_1_289_0,
author = {Huang, Hsiang-Ping},
title = {Commutators associated to a subfactor and its relative commutants},
journal = {Annales de l'Institut Fourier},
publisher = {Association des Annales de l'institut Fourier},
volume = {52},
number = {1},
year = {2002},
pages = {289-301},
doi = {10.5802/aif.1887},
zbl = {1021.46045},
mrnumber = {1881581},
language = {en},
url = {http://www.numdam.org/item/AIF_2002__52_1_289_0}
}

Huang, Hsiang-Ping. Commutators associated to a subfactor and its relative commutants. Annales de l'Institut Fourier, Tome 52 (2002) no. 1, pp. 289-301. doi : 10.5802/aif.1887. http://www.numdam.org/item/AIF_2002__52_1_289_0/

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