@article{AIHPA_1997__67_3_223_0, author = {Antoine, J.-P. and Inoue, A. and Ogi, H.}, title = {Standard generalized vectors for partial $O^\ast $-algebras}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {223--258}, publisher = {Gauthier-Villars}, volume = {67}, number = {3}, year = {1997}, mrnumber = {1472819}, zbl = {0899.47033}, language = {en}, url = {http://archive.numdam.org/item/AIHPA_1997__67_3_223_0/} }
TY - JOUR AU - Antoine, J.-P. AU - Inoue, A. AU - Ogi, H. TI - Standard generalized vectors for partial $O^\ast $-algebras JO - Annales de l'I.H.P. Physique théorique PY - 1997 SP - 223 EP - 258 VL - 67 IS - 3 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPA_1997__67_3_223_0/ LA - en ID - AIHPA_1997__67_3_223_0 ER -
%0 Journal Article %A Antoine, J.-P. %A Inoue, A. %A Ogi, H. %T Standard generalized vectors for partial $O^\ast $-algebras %J Annales de l'I.H.P. Physique théorique %D 1997 %P 223-258 %V 67 %N 3 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPA_1997__67_3_223_0/ %G en %F AIHPA_1997__67_3_223_0
Antoine, J.-P.; Inoue, A.; Ogi, H. Standard generalized vectors for partial $O^\ast $-algebras. Annales de l'I.H.P. Physique théorique, Tome 67 (1997) no. 3, pp. 223-258. http://archive.numdam.org/item/AIHPA_1997__67_3_223_0/
[1] Operator Algebras and Quantum Statistical Mechanics I, II, Springer-Verlag, Berlin, 1979.
and ,[2] Quantum Theory of Collective Phenomena, Clarendon Press, Oxford, 1986. | MR
,[3] On the use of modular groups in quantum field theory, Ann. Inst. H. Poincaré, Vol. 63, 1995, pp. 331-382. | Numdam | MR | Zbl
,[4] Unbounded Operator Algebras and Representation Theory, Akademie-Verlag, Berlin, 1990. | MR | Zbl
,[5] Local Quantum Physics: Fields, Particles, Algebras, Springer-Verlag, Berlin, 1993, 2d Revised ed. 1996. | MR | Zbl
,[6] 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
and ,[7] Topological algebras and their applications in Quantum Statistics, Wiss. Z. KMU-Leipzig, Math.-Naturwiss. R., Vol. 30, 1981, pp. 572-595. | MR | Zbl
,[8] Algebras of unbounded operators and quantum dynamics, Physica, Vol. 124 A, 1984, pp. 471-480. | MR | Zbl
,[9] Field algebras do not leave field domains invariant, Commun. Math. Phys., Vol. 102, 1988, pp. 687-692. | MR | Zbl
and ,[10] 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
, and ,[11] J-P. ANTOINE and 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, 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
and ,[13] Partial *-algebras of closable operators: A review, Reviews Math. Phys., Vol. 8, 1996, pp. 1-42. | MR | Zbl
, and ,[14] An unbounded generalization of the Tomita-Takesaki theory. I, Publ. RIMS, Kyoto Univ., Vol. 22, 1986, pp. 725-765. | MR | Zbl
,[15] An unbounded generalization of the Tomita-Takesaki theory. II, Publ. RIMS, Kyoto Univ., Vol. 23, 1987, pp. 673-726. | MR | Zbl
,[16] Modular structure of algebras of unbounded operators, Math. Proc. Camb. Phil. Soc., Vol. 111, 1992, pp. 369-386. | MR | Zbl
,[17] Cyclic generalized vectors for algebras of unbounded operators, Publ. RIMS, Kyoto Univ., Vol. 30, 1994, pp. 577-601. | MR | Zbl
and ,[18] Standard generalized vectors for algebras of unbounded operators, J. Math. Soc. Japan, Vol. 47, 1995, pp. 329-347. | MR | Zbl
,[19] Standard generalized vectors on the space of Hilbert-Schmidt operators, Ann. Inst. H. Poincaré, Vol. 63, 1995, pp. 177-210. | Numdam | MR | Zbl
, , and ,[20] Lectures on von Neumann Algebras, Abacus Press, Tunbridge Wells, (England), 1979. | MR
and ,[21] Tomita's theory of modular Hilbert-algebras and its application, Lect. Notes Math., Vol. 128, Springer-Verlag, Berlin, 1970. | MR | Zbl
,[22] A bounded operator approach to Tomita-Takesaki theory, Pacific J. Math., Vol. 69, 1977, pp. 187-221. | MR | Zbl
and ,[23] The standard form of von Neumann algebras, Math. Scand., Vol. 37, 1975, pp. 271-283. | MR | Zbl
,[24] Normal forms on partial O*-algebras, J. Math. Phys., Vol. 32, 1991, pp. 2074-2081. | MR | Zbl
and ,[25] A noncommutative probability theory, Trans. Amer. Math. Soc., Vol. 245, 1978, pp. 1-41. | MR | Zbl
and ,[26] Canonical commutation relations on the interval, J. Math. Phys., Vol. 28, 1987, pp. 174-177. | MR | Zbl
, and ,[27] Quasi*-algebras valued quantized fields, Ann. Inst. H. Poincaré, Vol. 46, 1987, pp. 175-185. | Numdam | MR | Zbl
and ,[28] States and representations of CQ*-algebras, Ann. Inst. H. Poincaré, Vol. 61, 1994, pp. 103-133. | Numdam | MR | Zbl
and ,