Canonical functional extensions on von Neumann algebras

Carlo Cecchini

Studia Mathematica (1999)

  • Volume: 135, Issue: 1, page 13-24
  • ISSN: 0039-3223

Abstract

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The topology and the structure of the set of the canonical extensions of positive, weakly continuous functionals from a von Neumann subalgebra M 0 to a von Neumann algebra M are described.

How to cite

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Cecchini, Carlo. "Canonical functional extensions on von Neumann algebras." Studia Mathematica 135.1 (1999): 13-24. <http://eudml.org/doc/216639>.

@article{Cecchini1999,
abstract = {The topology and the structure of the set of the canonical extensions of positive, weakly continuous functionals from a von Neumann subalgebra $M_0$ to a von Neumann algebra M are described.},
author = {Cecchini, Carlo},
journal = {Studia Mathematica},
keywords = {extension of functionals from subalgebra; positive selfdual cone; Connes cocycle; canonical functional extension; pointwise convergence; Radon-Nikodým derivatives},
language = {eng},
number = {1},
pages = {13-24},
title = {Canonical functional extensions on von Neumann algebras},
url = {http://eudml.org/doc/216639},
volume = {135},
year = {1999},
}

TY - JOUR
AU - Cecchini, Carlo
TI - Canonical functional extensions on von Neumann algebras
JO - Studia Mathematica
PY - 1999
VL - 135
IS - 1
SP - 13
EP - 24
AB - The topology and the structure of the set of the canonical extensions of positive, weakly continuous functionals from a von Neumann subalgebra $M_0$ to a von Neumann algebra M are described.
LA - eng
KW - extension of functionals from subalgebra; positive selfdual cone; Connes cocycle; canonical functional extension; pointwise convergence; Radon-Nikodým derivatives
UR - http://eudml.org/doc/216639
ER -

References

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  1. [1] L. Accardi and C. Cecchini, Conditional expectations in von Neumann algebras and a theorem of Takesaki, J. Funct. Anal. 45 (1982), 245-273. Zbl0483.46043
  2. [2] H. Araki, Some properties of modular conjugation operator of von Neumann algebras and a noncommutative Radon-Nikodym theorem with a chain rule, Pacific J. Math. 50 (1974), 309-354. Zbl0287.46074
  3. [3] C. Cecchini, An abstract characterization of ω-conditional expectations, Math. Scand. 66 (1990), 155-160. Zbl0748.46033
  4. [4] C. Cecchini and D. Petz, State extensions and a Radon-Nikodym theorem for conditional expectations on von Neumann algebras, Pacific J. Math. 138 (1989), 9-23. 
  5. [5] C. Cecchini and D. Petz, Classes of conditional expectations over von Neumann algebras, J. Funct. Anal. 92 (1990), 8-29. 
  6. [6] F. Combes et C. Delaroche, Groupe modulaire d'une espérance conditionnelle dans une algèbre de von Neumann, Bull. Soc. Math. France 103 (1975), 385-426 (1976). Zbl0321.46050
  7. [7] A. Connes, Sur le théorème de Radon-Nikodym pour les poids normaux fidèles semifinis, ibid. 97 (1973), 253-258. 

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