Standard generalized vectors for partial O*-algebras

J.-P. Antoine; A. Inoue; H. Ogi

Annales de l'I.H.P. Physique théorique (1997)

  • Volume: 67, Issue: 3, page 223-258
  • ISSN: 0246-0211

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Antoine, J.-P., Inoue, A., and Ogi, H.. "Standard generalized vectors for partial O*-algebras." Annales de l'I.H.P. Physique théorique 67.3 (1997): 223-258. <http://eudml.org/doc/76769>.

@article{Antoine1997,
author = {Antoine, J.-P., Inoue, A., Ogi, H.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {partial -algebras; partial -algebras; generalized vectors; KMS condition},
language = {eng},
number = {3},
pages = {223-258},
publisher = {Gauthier-Villars},
title = {Standard generalized vectors for partial O*-algebras},
url = {http://eudml.org/doc/76769},
volume = {67},
year = {1997},
}

TY - JOUR
AU - Antoine, J.-P.
AU - Inoue, A.
AU - Ogi, H.
TI - Standard generalized vectors for partial O*-algebras
JO - Annales de l'I.H.P. Physique théorique
PY - 1997
PB - Gauthier-Villars
VL - 67
IS - 3
SP - 223
EP - 258
LA - eng
KW - partial -algebras; partial -algebras; generalized vectors; KMS condition
UR - http://eudml.org/doc/76769
ER -

References

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  1. [1] Q. Bratteli and D. Robinson, Operator Algebras and Quantum Statistical Mechanics I, II, Springer-Verlag, Berlin, 1979. Zbl0421.46048
  2. [2] G.L. Sewell, Quantum Theory of Collective Phenomena, Clarendon Press, Oxford, 1986. MR944531
  3. [3] H.J. Borchers, On the use of modular groups in quantum field theory, Ann. Inst. H. Poincaré, Vol. 63, 1995, pp. 331-382. Zbl0838.46059MR1367142
  4. [4] K. Schmüdgen, Unbounded Operator Algebras and Representation Theory, Akademie–Verlag, Berlin, 1990. Zbl0697.47048MR1056697
  5. [5] R. Haag, Local Quantum Physics: Fields, Particles, Algebras, Springer-Verlag, Berlin, 1993, 2d Revised ed. 1996. Zbl0777.46037MR1405610
  6. [6] W. Thirring and A. Wehrl, On the mathematical structure of the B.C.S.-model. I, II, Commun. Math. Phys., Vol. 4, 1967, pp. 303-314; Vol. 7, 1968, pp. 181-189. Zbl0163.23302MR214345
  7. [7] G. Lassner, Topological algebras and their applications in Quantum Statistics, Wiss. Z. KMU-Leipzig, Math.-Naturwiss. R., Vol. 30, 1981, pp. 572-595. Zbl0483.47027MR655241
  8. [8] G. Lassner, Algebras of unbounded operators and quantum dynamics, Physica, Vol. 124 A, 1984, pp. 471-480. Zbl0599.47072MR759198
  9. [9] S.S. Horuzhy and A.V. Voronin, Field algebras do not leave field domains invariant, Commun. Math. Phys., Vol. 102, 1988, pp. 687-692. Zbl0597.47028MR824097
  10. [10] G. Epifanio, T. Todorov and C. Trapani, Complete sets of compatible nonself-adjoint observables, Helv. Phys. Acta, Vol. 65, 1992, 1-10; Complete sets of compatible nonself-adjoint observables: an unbounded approach, J. Math. Phys., Vol. 37, 1996, pp. 1148-1160. Zbl0884.47022MR1377624
  11. [11] J-P. ANTOINE and W. Karwowski, Partial *-algebras of closed linear operators in Hilbert space, Publ. RIMS, Kyoto Univ., Vol. 21, 1985, 205-236 ; Add./Err. ibid., Vol. 22, 1986, pp. 507-511. Zbl0609.47058MR780895
  12. [12] J-P. ANTOINE, A. Inoue and C. Trapani, Partial *-algebras of closable operators. I. The basic theory and the abelian case. II. States and representations of partial *-algebras, Publ. RIMS, Kyoto Univ., Vol. 26, 1990, pp. 359-395; Vol. 27, 1991, pp. 399-430. Zbl0724.47020MR1047417
  13. [13] J-P. Antoine, A. Inoue and C. Trapani, Partial *-algebras of closable operators: A review, Reviews Math. Phys., Vol. 8, 1996, pp. 1-42. Zbl0857.47029MR1372514
  14. [14] A. Inoue, An unbounded generalization of the Tomita-Takesaki theory. I, Publ. RIMS, Kyoto Univ., Vol. 22, 1986, pp. 725-765. Zbl0624.47044MR871264
  15. [15] A. Inoue, An unbounded generalization of the Tomita-Takesaki theory. II, Publ. RIMS, Kyoto Univ., Vol. 23, 1987, pp. 673-726. Zbl0641.47050MR918520
  16. [16] A. Inoue, Modular structure of algebras of unbounded operators, Math. Proc. Camb. Phil. Soc., Vol. 111, 1992, pp. 369-386. Zbl0771.47025MR1142756
  17. [17] A. Inoue and W. Karwowski, Cyclic generalized vectors for algebras of unbounded operators, Publ. RIMS, Kyoto Univ., Vol. 30, 1994, pp. 577-601. Zbl0836.47036MR1308958
  18. [18] A. Inoue, Standard generalized vectors for algebras of unbounded operators, J. Math. Soc. Japan, Vol. 47, 1995, pp. 329-347. Zbl0884.47023MR1317285
  19. [19] J-P. Antoine, A. Inoue, H. Ogi and C. Trapani, Standard generalized vectors on the space of Hilbert-Schmidt operators, Ann. Inst. H. Poincaré, Vol. 63, 1995, pp. 177-210. Zbl0831.47035MR1357495
  20. [20] S. Stratila and L. Zsidó, Lectures on von Neumann Algebras, Abacus Press, Tunbridge Wells, (England), 1979. Zbl0391.46048MR526399
  21. [21] M. Takesaki, Tomita's theory of modular Hilbert-algebras and its application, Lect. Notes Math., Vol. 128, Springer-Verlag, Berlin, 1970. Zbl0193.42502MR270168
  22. [22] M.A. Rieffel and A. Van Daele, A bounded operator approach to Tomita-Takesaki theory, Pacific J. Math., Vol. 69, 1977, pp. 187-221. Zbl0347.46073MR438147
  23. [23] U. Haagerup, The standard form of von Neumann algebras, Math. Scand., Vol. 37, 1975, pp. 271-283. Zbl0304.46044MR407615
  24. [24] J-P. Antoine and A. Inoue, Normal forms on partial O*-algebras, J. Math. Phys., Vol. 32, 1991, pp. 2074-2081. Zbl0770.47025MR1123597
  25. [25] S.P. Gudder and R.L. Hudson, A noncommutative probability theory, Trans. Amer. Math. Soc., Vol. 245, 1978, pp. 1-41. Zbl0407.46057MR511398
  26. [26] G. Lassner, G.A. Lassner and C. Trapani, Canonical commutation relations on the interval, J. Math. Phys., Vol. 28, 1987, pp. 174-177. Zbl0647.47051MR870115
  27. [27] G. Epifanio and C. Trapani, Quasi*-algebras valued quantized fields, Ann. Inst. H. Poincaré, Vol. 46, 1987, pp. 175-185. Zbl0617.46073MR887146
  28. [28] F. Bagarello and C. Trapani, States and representations of CQ*-algebras, Ann. Inst. H. Poincaré, Vol. 61, 1994, pp. 103-133. Zbl0820.46053MR1303188

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