Finite sums of commutators in C * -algebras

Thierry Fack

Annales de l'institut Fourier (1982)

  • Volume: 32, Issue: 1, page 129-137
  • ISSN: 0373-0956

Abstract

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We prove that for many C * -algebras, the null space of all finite traces is spanned by finite sums of commutators.

How to cite

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Fack, Thierry. "Finite sums of commutators in $C^*$-algebras." Annales de l'institut Fourier 32.1 (1982): 129-137. <http://eudml.org/doc/74522>.

@article{Fack1982,
abstract = {We prove that for many $C^*$-algebras, the null space of all finite traces is spanned by finite sums of commutators.},
author = {Fack, Thierry},
journal = {Annales de l'institut Fourier},
keywords = {finite traces; finite sums of commutators},
language = {eng},
number = {1},
pages = {129-137},
publisher = {Association des Annales de l'Institut Fourier},
title = {Finite sums of commutators in $C^*$-algebras},
url = {http://eudml.org/doc/74522},
volume = {32},
year = {1982},
}

TY - JOUR
AU - Fack, Thierry
TI - Finite sums of commutators in $C^*$-algebras
JO - Annales de l'institut Fourier
PY - 1982
PB - Association des Annales de l'Institut Fourier
VL - 32
IS - 1
SP - 129
EP - 137
AB - We prove that for many $C^*$-algebras, the null space of all finite traces is spanned by finite sums of commutators.
LA - eng
KW - finite traces; finite sums of commutators
UR - http://eudml.org/doc/74522
ER -

References

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  1. [1] J. CUNTZ, The structure of multiplication and addition in simple C*-algebras, Math. Scand., 40 (1977). Zbl0372.46063MR58 #17862
  2. [2] J. CUNTZ, A class of C*-algebras and topological Markov chains II : Reducible Markov chains and the Ext-functor for C*-algebras, Preprint Univ. Heidelberg, n° 57 (March 1980). Zbl0434.46045
  3. [3] J. CUNTZ and W. KRIEGER, A class of C*-algebras and topological Markov chains, Inventiones Math., 56 (1980), 251-268. Zbl0434.46045MR82f:46073a
  4. [4] J. CUNTZ and G.K. PEDERSEN, Equivalence and traces on C*-algebras, J. Functional Analysis, to appear. Zbl0427.46042
  5. [5] E.G. EFFROS, Dimensions and C*-algebras, Preprint UCLA (1980). 
  6. [6] T. FACK et P. DE LA HARPE, Sommes de commutateurs dans les algèbres de von Neumann finies continues, Ann. Inst. Fourier, Grenoble, 30,3 (1980), 49-73. Zbl0425.46046MR81m:46085
  7. [7] G.K. PEDERSEN, C*-algebras and their Automorphism Groups, Academic Press, New-York (1979). Zbl0416.46043MR81e:46037
  8. [8] G.K. PEDERSEN and N.H. PETERSEN, Ideals in a C*-algebra, Math. Scand., 27 (1970), 193-204. Zbl0218.46056MR46 #7911

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