Standard generalized vectors for partial O * -algebras
Annales de l'I.H.P. Physique théorique, Volume 67 (1997) no. 3, pp. 223-258.
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     title = {Standard generalized vectors for partial $O^\ast $-algebras},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
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     url = {http://archive.numdam.org/item/AIHPA_1997__67_3_223_0/}
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Antoine, J.-P.; Inoue, A.; Ogi, H. Standard generalized vectors for partial $O^\ast $-algebras. Annales de l'I.H.P. Physique théorique, Volume 67 (1997) no. 3, pp. 223-258. http://archive.numdam.org/item/AIHPA_1997__67_3_223_0/

[1] Q. Bratteli and D. Robinson, Operator Algebras and Quantum Statistical Mechanics I, II, Springer-Verlag, Berlin, 1979.

[2] G.L. Sewell, Quantum Theory of Collective Phenomena, Clarendon Press, Oxford, 1986. | MR

[3] H.J. Borchers, On the use of modular groups in quantum field theory, Ann. Inst. H. Poincaré, Vol. 63, 1995, pp. 331-382. | Numdam | MR | Zbl

[4] K. Schmüdgen, Unbounded Operator Algebras and Representation Theory, Akademie-Verlag, Berlin, 1990. | MR | Zbl

[5] R. Haag, Local Quantum Physics: Fields, Particles, Algebras, Springer-Verlag, Berlin, 1993, 2d Revised ed. 1996. | MR | Zbl

[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. | MR | Zbl

[7] G. Lassner, Topological algebras and their applications in Quantum Statistics, Wiss. Z. KMU-Leipzig, Math.-Naturwiss. R., Vol. 30, 1981, pp. 572-595. | MR | Zbl

[8] G. Lassner, Algebras of unbounded operators and quantum dynamics, Physica, Vol. 124 A, 1984, pp. 471-480. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[14] A. Inoue, An unbounded generalization of the Tomita-Takesaki theory. I, Publ. RIMS, Kyoto Univ., Vol. 22, 1986, pp. 725-765. | MR | Zbl

[15] A. Inoue, An unbounded generalization of the Tomita-Takesaki theory. II, Publ. RIMS, Kyoto Univ., Vol. 23, 1987, pp. 673-726. | MR | Zbl

[16] A. Inoue, Modular structure of algebras of unbounded operators, Math. Proc. Camb. Phil. Soc., Vol. 111, 1992, pp. 369-386. | MR | Zbl

[17] A. Inoue and W. Karwowski, Cyclic generalized vectors for algebras of unbounded operators, Publ. RIMS, Kyoto Univ., Vol. 30, 1994, pp. 577-601. | MR | Zbl

[18] A. Inoue, Standard generalized vectors for algebras of unbounded operators, J. Math. Soc. Japan, Vol. 47, 1995, pp. 329-347. | MR | Zbl

[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. | Numdam | MR | Zbl

[20] S. Stratila and L. Zsidó, Lectures on von Neumann Algebras, Abacus Press, Tunbridge Wells, (England), 1979. | MR

[21] M. Takesaki, Tomita's theory of modular Hilbert-algebras and its application, Lect. Notes Math., Vol. 128, Springer-Verlag, Berlin, 1970. | MR | Zbl

[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. | MR | Zbl

[23] U. Haagerup, The standard form of von Neumann algebras, Math. Scand., Vol. 37, 1975, pp. 271-283. | MR | Zbl

[24] J-P. Antoine and A. Inoue, Normal forms on partial O*-algebras, J. Math. Phys., Vol. 32, 1991, pp. 2074-2081. | MR | Zbl

[25] S.P. Gudder and R.L. Hudson, A noncommutative probability theory, Trans. Amer. Math. Soc., Vol. 245, 1978, pp. 1-41. | MR | Zbl

[26] G. Lassner, G.A. Lassner and C. Trapani, Canonical commutation relations on the interval, J. Math. Phys., Vol. 28, 1987, pp. 174-177. | MR | Zbl

[27] G. Epifanio and C. Trapani, Quasi*-algebras valued quantized fields, Ann. Inst. H. Poincaré, Vol. 46, 1987, pp. 175-185. | Numdam | MR | Zbl

[28] F. Bagarello and C. Trapani, States and representations of CQ*-algebras, Ann. Inst. H. Poincaré, Vol. 61, 1994, pp. 103-133. | Numdam | MR | Zbl