States and representations of CQ * -algebras
Bagarello, F. ; Trapani, C.
Annales de l'I.H.P. Physique théorique, Tome 61 (1994), p. 103-133 / Harvested from Numdam
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@article{AIHPA_1994__61_1_103_0,
     author = {Bagarello, F. and Trapani, C.},
     title = {States and representations of $CQ^\ast $-algebras},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {61},
     year = {1994},
     pages = {103-133},
     mrnumber = {1303188},
     zbl = {0820.46053},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1994__61_1_103_0}
}

Bagarello, F.; Trapani, C. States and representations of $CQ^\ast $-algebras. Annales de l'I.H.P. Physique théorique, Tome 61 (1994) pp. 103-133. http://gdmltest.u-ga.fr/item/AIHPA_1994__61_1_103_0/

[1] R. Haag and D. Kastler, An Algebraic Approach to Quantum Field Theory, J. Math. Phys., Vol. 5, 1964, pp. 848-861. | MR 165864 | Zbl 0139.46003

[2] W. Thirring and A. Wehrl, On the Mathematical Structure of the B.C.S.-Model, Commun. Math. Phys., Vol. 4, 1967, pp. 303-314. | MR 214345 | Zbl 0163.23302

[3] F. Bagarello and G. Morchio, Dynamics of Mean-Field Spin Models from Basic Results in Abstract Differential Equations, J. Statistical Phys., Vol. 66, 1992, pp. 849-866. | MR 1151983 | Zbl 0892.58090

[4] F. Bagarello and C. Trapani, "Almost" Mean Field Ising Model: an Algebraic Approach, J. Statistical Phys., Vol. 65, 1991, pp. 469-482. | MR 1137420 | Zbl 0945.82503

[5] F. Bagarello and C. Trapani, A Note on the Algebraic Approach to the Almost Mean Field Heisenberg Model, Il Nuovo Cimento, B (to appear). | MR 1281766

[6] G. Morchio and F. Strocchi, Long Range Dynamics and Broken Symmetries in Gauge Models. The Stückelberg-Kibble model, Commun. Math. Phys., Vol. 111, 1987, pp. 593-612. | MR 901156

[7] G. Morchio and F. Strocchi, Long Range Dynamics and Broken Symmetries in Gauge Models. The Schwinger Model, J. Math. Phys., Vol. 28, 1987, pp. 1912-1919. | MR 899197 | Zbl 0626.58043

[8] G. Epifanio and C. Trapani, Quasi *-Algebras valued Quantized Fields, Ann. Inst. H. Poincaré, Vol. 46, 1987, pp. 175-185. | Numdam | MR 887146 | Zbl 0617.46073

[9] R. Ascoli, G. Epifanio and A. Restivo, On the Mathematical Description of Quantized Fields, Commun. Math. Phys., Vol. 18, 1970, pp. 291-300. | MR 272300 | Zbl 0197.53502

[10] K. Fredenhagen and J. Hertel, Local Algebras of Observables and Pointlike Localized Fields, Commun. Math. Phys., Vol. 80, 1981, pp. 555-561. | MR 628511 | Zbl 0472.46051

[11] G. Lassner, Topological Algebras and their Applications in Quantum Statistics, Wiss. Z. KMU, Leipzig, Math.-Nat. R., Vol. 6, 1981, pp. 572-595. | MR 655241 | Zbl 0483.47027

[12] G. Lassner, Algebras of Unbounded Operators and Quantum Dynamics, Physica, Vol. 124A, 1984, pp. 471-480. | Zbl 0599.47072

[13] G. Lassner and G.A. Lassner, Qu *-Algebras and Twisted Product, Publ. RIMS, Kyoto Univ., Vol. 25, 1989, pp. 279-299. | MR 1003789 | Zbl 0695.47038

[14] G. Lassner, G.A. Lassner and C. Trapani, Canonical Commutation Relations on the Interval, J. Math. Phys., Vol. 28, 1987, pp. 174-177. | MR 870115 | Zbl 0647.47051

[15] K.D. Kürsten, The Completion of the Maximal Op*-Algebra on a Frechet Domain, Publ. RIMS, Kyoto Univ., Vol. 22, 1986, pp. 151-175. | MR 834354 | Zbl 0607.47043

[16] K.D. Kürsten, Duality for Maximal Op*-Algebras on Frechet Domains, Publ. RIMS, Kyoto Univ., Vol. 24, 1988, pp. 585-620. | MR 976761 | Zbl 0683.47032

[17] C. Trapani, States and Derivations on Quasi *-Algebras, J. Math. Phys., Vol. 29, 1988, pp. 1885-1890. | MR 955193 | Zbl 0649.47037

[18] J.-P. Antoine and W. Karwowski, Partial *-Algebras of Closed Linear Operators in Hilbert Space, Publ. RIMS, Kyoto Univ., Vol. 21, 1985, pp. 205-236. | MR 780895 | Zbl 0609.47058

[19] J.-P. Antoine and F. Mathot, Partial *-Algebras of Closed Operators and their Commutants, I. General Structure, Ann. Inst. Henri Poincaré, Vol. 46, 1987, pp. 299-324. | Numdam | MR 892367 | Zbl 0629.46048

[20] J.-P. Antoine, F. Mathot and C. Trapani, Partial *-Algebras of Closed Operators and their Commutants, II. Commutants and Bicommutants, Vol. 46, 1987, pp. 325-351. | Numdam | MR 892368 | Zbl 0629.46049

[21] J.-P. Antoine, A. Inoue and C. Trapani, Partial *-Algebras of Closable Operators, I: The Basic Theory and the Abelian Case, Publ. RIMS, Kyoto Univ., Vol. 26, 1990, pp. 359-395. | MR 1047417 | Zbl 0724.47020

[22] J.-P. Antoine, A. Inoue and C. Trapani, Partial *-Algebras of Closable Operators, II: States and Representations of Partial *-Algebras, Publ. RIMS, Kyoto University, Vol. 27, 1991, pp. 399-430. | MR 1121245 | Zbl 0749.47030

[23] K. Schmüdgen, Unbounded Operator Algebras and Representations Theory, Birkhauser, Basel, 1990. | MR 1056697

[24] P.G. Dixon, Generalized B *-Algebras, Proc. London Math. Soc., Vol. 21, 1970, pp. 693-715. | MR 278079 | Zbl 0205.42604

[25] G.R. Allan, On a Class of Locally Convex Algebras, Proc. London Math. Soc., Vol. 17, 1967, pp. 91-114. | MR 205102 | Zbl 0147.33503

[26] K. Schmüdgen, Lokal Multiplicativ Konvexe Op *-Algebren, Math. Nach., Vol. 85, 1978, pp. 161-170. | MR 517647 | Zbl 0319.46035

[27] G. Epifanio and C. Trapani, V *-Algebras: a Particular Class of Unbounded Operator Algebras, J. Math. Phys., Vol. 25, 1984, p. 2633. | MR 756559 | Zbl 0556.47026

[28] M. Reed and B. Simon, Methods of Modern Mathematical Physics, I, Academic Press, New York, 1980. | MR 751959

[29] R.S. Doran and V.A. Belfi, Characterizations of C*-Algebras, Pure and Applied Mathematics, M. Dekker, Inc., New York, Basel, 1986. | MR 831427 | Zbl 0597.46056

[30] A. Grossmann, Elementary Properties of Nested Hilbert Spaces, Commun. Math. Phys., Vol. 2, 1966, pp. 1-30. | MR 196460 | Zbl 0134.31701

[31] J. Dixmier, Les C*-algèbres et leurs représentations, Gauthier-Villars, Paris, 1964. | MR 171173 | Zbl 0152.32902

[32] S. Sakai, C*-Algebras and W*-Algebras, Springer-Verlag, 1971. | MR 442701 | Zbl 0219.46042

[33] R.V. Kadison and J.R. Ringrose, Fundamentals of the Theory of Operator Algebras, I et II, Academic Press, New York, 1983. | MR 719020 | Zbl 0518.46046

[34] O. Bratteli and D.W. Robinson, Operator Algebras and Quantum Statistical Mechanics, I, Springer Verlag, New York, 1979. | MR 611508 | Zbl 0421.46048

[35] J.-P. Antoine, in Spontaneous Symmetry Breakdown and Related Subjects, p. 247; L. MICHEL, J. MOZRZYMAS and A. PEKALSKI, eds., World Scientific, Singapore, 1985. | MR 835498

[36] J.-P. Antoine, Y. Soulet and C. Trapani, Weights on Partial *-Algebras, Preprint. | MR 1336486

[37] C.E. Rickart, General Theory of Banach Algebras, van Nostrand, Princeton, 1960. | MR 115101 | Zbl 0095.09702

[38] I.M. Gel'Fand and Ya. Vilenkin, Generalized Functions, IV, Academic Press, New York, 1964.

[39] J.-P. Antoine and W. Karwowski, Bull. Acad. Pol. Sci., Theor. Phys., Vol. XXVII, 1979, p. 223. | MR 652806 | Zbl 0493.46025

[40] F. Debacker-Mathot, Some Operator Algebras in Nested Hilbert Spaces, Commun. Math. Phys., Vol. 42, 1975, pp. 183-193. | MR 467344 | Zbl 0303.46061

[41] J.-P. Antoine and A. Grossmann, Partial Inner Product Spaces I, II, J. Funct. Anal., Vol. 23, 1976, pp. 369-378; Vol. 23, 1976, pp. 379-391. | Zbl 0359.46020

[42] J.-P. Antoine, Partial Inner Product Spaces. IV. Topological Considerations, J. Math. Phys., Vol. 21, 1980, p. 2067. | MR 579203 | Zbl 0477.46006

[43] G. Köthe, Topological Vector Spaces, I, Springer-Verlag, Berlin, New York, 1983. | MR 248498

[44] K.D. Kürsten, On Topological Properties of Domains of Unbounded Operator Algebras, Proc. II Int. Conf. Operator Algebras, Ideals and Their Applications in Theoretical Physics, Teubner, Leipzig, 1984, p. 105-107. | MR 763529 | Zbl 0544.47040

[45] G. Lassner and G.A. Lassner, On the Continuity of Entropy, Rep. Math. Phys., Vol. 15, 1975, p. 41. | MR 551129 | Zbl 0426.47023

[46] R. Jost, The General Theory of Quantized Fields, American Mathematical Society, Providence, 1965. | MR 177667 | Zbl 0127.19105

[47] S.S. Horuzhy, Introduction to Algebraic Quantum Field Theory, Kluwer Academic Publishers, Dordrecht, 1990. | MR 1063850

[48] J.F. Colombeau, New Generalized Functions and Multiplication of Distributions, North-Holland, Amsterdam, 1984. | MR 738781 | Zbl 0532.46019