On the Lebesgue decomposition of the normal states of a JBW-algebra
Mathematica Bohemica (1992)
- Volume: 117, Issue: 2, page 185-193
- ISSN: 0862-7959
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topDubois, Jacques, and Hadjou, Brahim. "On the Lebesgue decomposition of the normal states of a JBW-algebra." Mathematica Bohemica 117.2 (1992): 185-193. <http://eudml.org/doc/29054>.
@article{Dubois1992,
abstract = {In this article, a theorem is proved asserting that any linear functional defined on a JBW-algebra admits a Lebesque decomposition with respect to any normal state defined on the algebra. Then we show that the positivity (and the unicity) of this decomposition is insured for the trace states defined on the algebra. In fact, this property can be used to give a new characterization of the trace states amoungst all the normal states.},
author = {Dubois, Jacques, Hadjou, Brahim},
journal = {Mathematica Bohemica},
keywords = {linear functional; JBW-algebra; Lebesgue decomposition; normal state; trace states; state; Lebesgue decomposition of a linear functional with respect to another linear functional; support of linear functional; linear functional; JBW-algebra; Lebesgue decomposition; normal state; trace states},
language = {eng},
number = {2},
pages = {185-193},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the Lebesgue decomposition of the normal states of a JBW-algebra},
url = {http://eudml.org/doc/29054},
volume = {117},
year = {1992},
}
TY - JOUR
AU - Dubois, Jacques
AU - Hadjou, Brahim
TI - On the Lebesgue decomposition of the normal states of a JBW-algebra
JO - Mathematica Bohemica
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 117
IS - 2
SP - 185
EP - 193
AB - In this article, a theorem is proved asserting that any linear functional defined on a JBW-algebra admits a Lebesque decomposition with respect to any normal state defined on the algebra. Then we show that the positivity (and the unicity) of this decomposition is insured for the trace states defined on the algebra. In fact, this property can be used to give a new characterization of the trace states amoungst all the normal states.
LA - eng
KW - linear functional; JBW-algebra; Lebesgue decomposition; normal state; trace states; state; Lebesgue decomposition of a linear functional with respect to another linear functional; support of linear functional; linear functional; JBW-algebra; Lebesgue decomposition; normal state; trace states
UR - http://eudml.org/doc/29054
ER -
References
top- E. M. Alfsen, F. W. Shultz, 10.1112/plms/s3-38.3.497, Pгoc. London Math. Soc. 38 (1979), 497-516. (1979) Zbl0404.46028MR0532984DOI10.1112/plms/s3-38.3.497
- S. A. Ajupov, 10.1016/0022-1236(89)90100-6, J. of Functional Analysis 84 (1989), 312-321. (1989) MR1001463DOI10.1016/0022-1236(89)90100-6
- L. J. Bunce, J. D. Wright, Continuity and Linear Extensions of Quantum Measures on Jordan Operatoг Algebras, Preprint. To appear in Math. Scandinavia.
- A. M. Gleason, Measures on the closed subspaces of a Hilbeгt space, J. Math. Mech. 6 (1957), 885-893. (1957) MR0096113
- H. Hanche-Olsen, E. Størmer, Jordan Operator Algebras, Pitman, Boston, 1984. (1984) MR0755003
- V. Palko, On the Lebesgue Decomposition of Gleason Measures, Časopis pro pěstování Mat. 112 no. 1 (1987), 1-5. (1987) Zbl0621.46058MR0880929
- G. K. Pederson, E. Størmer, 10.4153/CJM-1982-024-7, Can. J. Math. 34 (1982), 370-373. (1982) MR0658972DOI10.4153/CJM-1982-024-7
- G. T. Rüttimann, C. Schindler, 10.1093/qmath/37.3.321, Quart. J. Math. Oxford 31 no. 2 (1986), 321-345. (1986) MR0854631DOI10.1093/qmath/37.3.321
- F. W. Shultz, 10.1016/0022-1236(79)90010-7, J. Funct. Analysis 31 (1979), 360-376. (1979) Zbl0421.46043MR0531138DOI10.1016/0022-1236(79)90010-7
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