Sums of commutators in ideals and modules of type II factors

J. Dykema, Kenneth; J. Kalton, Nigel

doi:10.5802/aif.2118

Sums of commutators in ideals and modules of type II factors
[Sommes des commutateurs dans les idéaux et les modules de facteurs de type II]

J. Dykema, Kenneth ¹ ; J. Kalton, Nigel

¹ Texas A\&M University, department of mathematics, College Station TX 77843-3368 (USA), University of Missouri, department of mathematics, Columbia MO 65211 (USA)

Annales de l'Institut Fourier, Tome 55 (2005) no. 3, pp. 931-971.

Résumé
Abstract

Soit $ℳ$ un facteur de type II $_{\infty}$ ou II $_{1}$ avec prédual séparable et soit $\bar{ℳ}$ l’algèbre d’operateurs $τ$ -mesurable et affilié avec $ℳ$ . Nous caractérisons l’espace des sommes de commutateurs $[ℐ, 𝒥]$ pour tous sous- $(ℳ, ℳ)$ -bimodules $ℐ$ et $𝒥$ de $\bar{ℳ}$ .

Let $ℳ$ be a factor of type II $_{\infty}$ or II $_{1}$ having separable predual and let $\bar{ℳ}$ be the algebra of affiliated $τ$ -measurable operators. We characterize the commutator space $[ℐ, 𝒥]$ for sub- $(ℳ, ℳ)$ - bimodules $ℐ$ and $𝒥$ of $\bar{ℳ}$ .

MR Zbl

DOI : 10.5802/aif.2118

Classification : 46L10, 46L52
Keywords: commutators, type II factors, Brown measure, noncommutative function spaces
Mot clés : commutateurs, facteurs de type II, mesure de Brown, l'espace de fonctions non commutatives

Affiliations des auteurs :

J. Dykema, Kenneth ¹ ; J. Kalton, Nigel

¹ Texas A\&M University, department of mathematics, College Station TX 77843-3368 (USA), University of Missouri, department of mathematics, Columbia MO 65211 (USA)

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J. Dykema, Kenneth; J. Kalton, Nigel. Sums of commutators in ideals and modules of type II factors. Annales de l'Institut Fourier, Tome 55 (2005) no. 3, pp. 931-971. doi : 10.5802/aif.2118. http://www.numdam.org/articles/10.5802/aif.2118/

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