Centrally determined states on von Neumann algebras

Jan Hamhalter

Mathematica Bohemica (1992)

  • Volume: 117, Issue: 2, page 195-196
  • ISSN: 0862-7959

Abstract

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It is shown that every von Neumann algebra whose centre determines the state space is already abelian.

How to cite

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Hamhalter, Jan. "Centrally determined states on von Neumann algebras." Mathematica Bohemica 117.2 (1992): 195-196. <http://eudml.org/doc/29061>.

@article{Hamhalter1992,
abstract = {It is shown that every von Neumann algebra whose centre determines the state space is already abelian.},
author = {Hamhalter, Jan},
journal = {Mathematica Bohemica},
keywords = {von Neumann algebra; centrally determined state space; state space of operator algebras; noncommutative Radon-Nikodym theorem; von Neumann algebra; centrally determined state space},
language = {eng},
number = {2},
pages = {195-196},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Centrally determined states on von Neumann algebras},
url = {http://eudml.org/doc/29061},
volume = {117},
year = {1992},
}

TY - JOUR
AU - Hamhalter, Jan
TI - Centrally determined states on von Neumann algebras
JO - Mathematica Bohemica
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 117
IS - 2
SP - 195
EP - 196
AB - It is shown that every von Neumann algebra whose centre determines the state space is already abelian.
LA - eng
KW - von Neumann algebra; centrally determined state space; state space of operator algebras; noncommutative Radon-Nikodym theorem; von Neumann algebra; centrally determined state space
UR - http://eudml.org/doc/29061
ER -

References

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  1. R. V. Kadison J. R. Ringrose, Fundamentals of the Theory of Operator Algebras, Academic Press, 1986. (1986) MR0859186
  2. M. Navara, Stavový Prostor Kvantových Logik, Ph.d. thesis, Prague, 1987. (1987) 
  3. M. Navara P. Pták, On the Radon-Nikodym property in quantum logics, Proceedings of the Conference Topology and Measure VI, Wardeminde, 1991, to appear. (1991) MR1226290
  4. Proceedings of the 2nd Winter School on Measure Theory, Liptovský Ján, January 1990. (1990) 
  5. S. Sakai, 10.1090/S0002-9904-1965-11265-4, Bull. Amer. Math. Soc. 71 (1965), 149-151. (1965) MR0174992DOI10.1090/S0002-9904-1965-11265-4
  6. V. Varadarajan, Geometry of Quantum Theory I, Van Nostrand, Princeton, New Jersey, 1968. (1968) MR0471674

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