Sums of commutators in ideals and modules of type II factors

Kenneth J. Dykema[1]; Nigel J. Kalton

  • [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 (2005)

  • Volume: 55, Issue: 3, page 931-971
  • ISSN: 0373-0956

Abstract

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Let ℳ be a factor of type II ∞ or II 1 having separable predual and let 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 ℳ ¯ .

How to cite

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J. Dykema, Kenneth, and J. Kalton, Nigel. "Sums of commutators in ideals and modules of type II factors." Annales de l’institut Fourier 55.3 (2005): 931-971. <http://eudml.org/doc/116212>.

@article{J2005,
abstract = {Let $\{\mathcal \{M\}\}$ be a factor of type II$_\infty $ or II$_1$ having separable predual and let $\overline\{\mathcal \{M\}\}$ be the algebra of affiliated $\tau $-measurable operators. We characterize the commutator space $[\{\mathcal \{I\}\},\{\mathcal \{J\}\}]$ for sub-$(\{\mathcal \{M\}\},\{\mathcal \{M\}\})$- bimodules $\{\mathcal \{I\}\}$ and $\{\mathcal \{J\}\}$ of $\overline\{\mathcal \{M\}\}$.},
affiliation = {Texas A&M University, department of mathematics, College Station TX 77843-3368 (USA), University of Missouri, department of mathematics, Columbia MO 65211 (USA)},
author = {J. Dykema, Kenneth, J. Kalton, Nigel},
journal = {Annales de l’institut Fourier},
keywords = {commutators; type II factors; Brown measure; noncommutative function spaces},
language = {eng},
number = {3},
pages = {931-971},
publisher = {Association des Annales de l'Institut Fourier},
title = {Sums of commutators in ideals and modules of type II factors},
url = {http://eudml.org/doc/116212},
volume = {55},
year = {2005},
}

TY - JOUR
AU - J. Dykema, Kenneth
AU - J. Kalton, Nigel
TI - Sums of commutators in ideals and modules of type II factors
JO - Annales de l’institut Fourier
PY - 2005
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 3
SP - 931
EP - 971
AB - Let ${\mathcal {M}}$ be a factor of type II$_\infty $ or II$_1$ having separable predual and let $\overline{\mathcal {M}}$ be the algebra of affiliated $\tau $-measurable operators. We characterize the commutator space $[{\mathcal {I}},{\mathcal {J}}]$ for sub-$({\mathcal {M}},{\mathcal {M}})$- bimodules ${\mathcal {I}}$ and ${\mathcal {J}}$ of $\overline{\mathcal {M}}$.
LA - eng
KW - commutators; type II factors; Brown measure; noncommutative function spaces
UR - http://eudml.org/doc/116212
ER -

References

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