States and representations of CQ*-algebras

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1. [1] R. Haag and D. Kastler, An Algebraic Approach to Quantum Field Theory, J. Math. Phys., Vol. 5, 1964, pp. 848-861. Zbl0139.46003MR165864
2. [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. Zbl0163.23302MR214345
3. [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. Zbl0892.58090MR1151983
4. [4] F. Bagarello and C. Trapani, "Almost" Mean Field Ising Model: an Algebraic Approach, J. Statistical Phys., Vol. 65, 1991, pp. 469-482. Zbl0945.82503MR1137420
5. [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). Zbl0945.82503MR1281766
6. [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. Zbl0626.58043MR901156
7. [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. Zbl0626.58043MR899197
8. [8] G. Epifanio and C. Trapani, Quasi *-Algebras valued Quantized Fields, Ann. Inst. H. Poincaré, Vol. 46, 1987, pp. 175-185. Zbl0617.46073MR887146
9. [9] R. Ascoli, G. Epifanio and A. Restivo, On the Mathematical Description of Quantized Fields, Commun. Math. Phys., Vol. 18, 1970, pp. 291-300. Zbl0197.53502MR272300
10. [10] K. Fredenhagen and J. Hertel, Local Algebras of Observables and Pointlike Localized Fields, Commun. Math. Phys., Vol. 80, 1981, pp. 555-561. Zbl0472.46051MR628511
11. [11] G. Lassner, Topological Algebras and their Applications in Quantum Statistics, Wiss. Z. KMU, Leipzig, Math.-Nat. R., Vol. 6, 1981, pp. 572-595. Zbl0483.47027MR655241
12. [12] G. Lassner, Algebras of Unbounded Operators and Quantum Dynamics, Physica, Vol. 124A, 1984, pp. 471-480. Zbl0599.47072
13. [13] G. Lassner and G.A. Lassner, Qu *-Algebras and Twisted Product, Publ. RIMS, Kyoto Univ., Vol. 25, 1989, pp. 279-299. Zbl0695.47038MR1003789
14. [14] 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
15. [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. Zbl0607.47043MR834354
16. [16] K.D. Kürsten, Duality for Maximal Op*-Algebras on Frechet Domains, Publ. RIMS, Kyoto Univ., Vol. 24, 1988, pp. 585-620. Zbl0683.47032MR976761
17. [17] C. Trapani, States and Derivations on Quasi *-Algebras, J. Math. Phys., Vol. 29, 1988, pp. 1885-1890. Zbl0649.47037MR955193
18. [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. Zbl0609.47058MR780895
19. [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. Zbl0629.46048MR892367
20. [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. Zbl0629.46049MR892368
21. [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. Zbl0724.47020MR1047417
22. [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. Zbl0749.47030MR1121245
23. [23] K. Schmüdgen, Unbounded Operator Algebras and Representations Theory, Birkhauser, Basel, 1990. MR1056697
24. [24] P.G. Dixon, Generalized B *-Algebras, Proc. London Math. Soc., Vol. 21, 1970, pp. 693-715. Zbl0205.42604MR278079
25. [25] G.R. Allan, On a Class of Locally Convex Algebras, Proc. London Math. Soc., Vol. 17, 1967, pp. 91-114. Zbl0147.33503MR205102
26. [26] K. Schmüdgen, Lokal Multiplicativ Konvexe Op *-Algebren, Math. Nach., Vol. 85, 1978, pp. 161-170. Zbl0319.46035MR517647
27. [27] G. Epifanio and C. Trapani, V *-Algebras: a Particular Class of Unbounded Operator Algebras, J. Math. Phys., Vol. 25, 1984, p. 2633. Zbl0556.47026MR756559
28. [28] M. Reed and B. Simon, Methods of Modern Mathematical Physics, I, Academic Press, New York, 1980. MR751959
29. [29] R.S. Doran and V.A. Belfi, Characterizations of C*-Algebras, Pure and Applied Mathematics, M. Dekker, Inc., New York, Basel, 1986. Zbl0597.46056MR831427
30. [30] A. Grossmann, Elementary Properties of Nested Hilbert Spaces, Commun. Math. Phys., Vol. 2, 1966, pp. 1-30. Zbl0134.31701MR196460
31. [31] J. Dixmier, Les C*-algèbres et leurs représentations, Gauthier-Villars, Paris, 1964. Zbl0152.32902MR171173
32. [32] S. Sakai, C*-Algebras and W*-Algebras, Springer-Verlag, 1971. Zbl0219.46042MR442701
33. [33] R.V. Kadison and J.R. Ringrose, Fundamentals of the Theory of Operator Algebras, I et II, Academic Press, New York, 1983. Zbl0518.46046MR719020
34. [34] O. Bratteli and D.W. Robinson, Operator Algebras and Quantum Statistical Mechanics, I, Springer Verlag, New York, 1979. Zbl0421.46048MR611508
35. [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. MR835498
36. [36] J.-P. Antoine, Y. Soulet and C. Trapani, Weights on Partial *-Algebras, Preprint. Zbl0888.46034MR1336486
37. [37] C.E. Rickart, General Theory of Banach Algebras, van Nostrand, Princeton, 1960. Zbl0095.09702MR115101
38. [38] I.M. Gel'fand and Ya. Vilenkin, Generalized Functions, IV, Academic Press, New York, 1964. 
39. [39] J.-P. Antoine and W. Karwowski, Bull. Acad. Pol. Sci., Theor. Phys., Vol. XXVII, 1979, p. 223. Zbl0493.46025MR652806
40. [40] F. Debacker-Mathot, Some Operator Algebras in Nested Hilbert Spaces, Commun. Math. Phys., Vol. 42, 1975, pp. 183-193. Zbl0303.46061MR467344
41. [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. Zbl0359.46020
42. [42] J.-P. Antoine, Partial Inner Product Spaces. IV. Topological Considerations, J. Math. Phys., Vol. 21, 1980, p. 2067. Zbl0477.46006MR579203
43. [43] G. Köthe, Topological Vector Spaces, I, Springer-Verlag, Berlin, New York, 1983. Zbl0179.17001MR248498
44. [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. Zbl0544.47040MR763529
45. [45] G. Lassner and G.A. Lassner, On the Continuity of Entropy, Rep. Math. Phys., Vol. 15, 1975, p. 41. Zbl0426.47023MR551129
46. [46] R. Jost, The General Theory of Quantized Fields, American Mathematical Society, Providence, 1965. Zbl0127.19105MR177667
47. [47] S.S. Horuzhy, Introduction to Algebraic Quantum Field Theory, Kluwer Academic Publishers, Dordrecht, 1990. MR1063850
48. [48] J.F. Colombeau, New Generalized Functions and Multiplication of Distributions, North-Holland, Amsterdam, 1984. Zbl0532.46019MR738781

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