@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}, pages = {103--133}, publisher = {Gauthier-Villars}, volume = {61}, number = {1}, year = {1994}, mrnumber = {1303188}, zbl = {0820.46053}, language = {en}, url = {http://archive.numdam.org/item/AIHPA_1994__61_1_103_0/} }
TY - JOUR AU - Bagarello, F. AU - Trapani, C. TI - States and representations of $CQ^\ast $-algebras JO - Annales de l'I.H.P. Physique théorique PY - 1994 SP - 103 EP - 133 VL - 61 IS - 1 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPA_1994__61_1_103_0/ LA - en ID - AIHPA_1994__61_1_103_0 ER -
Bagarello, F.; Trapani, C. States and representations of $CQ^\ast $-algebras. Annales de l'I.H.P. Physique théorique, Volume 61 (1994) no. 1, pp. 103-133. http://archive.numdam.org/item/AIHPA_1994__61_1_103_0/
[1] An Algebraic Approach to Quantum Field Theory, J. Math. Phys., Vol. 5, 1964, pp. 848-861. | MR | Zbl
and ,[2] On the Mathematical Structure of the B.C.S.-Model, Commun. Math. Phys., Vol. 4, 1967, pp. 303-314. | MR | Zbl
and ,[3] Dynamics of Mean-Field Spin Models from Basic Results in Abstract Differential Equations, J. Statistical Phys., Vol. 66, 1992, pp. 849-866. | MR | Zbl
and ,[4] "Almost" Mean Field Ising Model: an Algebraic Approach, J. Statistical Phys., Vol. 65, 1991, pp. 469-482. | MR | Zbl
and ,[5] A Note on the Algebraic Approach to the Almost Mean Field Heisenberg Model, Il Nuovo Cimento, B (to appear). | MR
and ,[6] Long Range Dynamics and Broken Symmetries in Gauge Models. The Stückelberg-Kibble model, Commun. Math. Phys., Vol. 111, 1987, pp. 593-612. | MR
and ,[7] Long Range Dynamics and Broken Symmetries in Gauge Models. The Schwinger Model, J. Math. Phys., Vol. 28, 1987, pp. 1912-1919. | MR | Zbl
and ,[8] Quasi *-Algebras valued Quantized Fields, Ann. Inst. H. Poincaré, Vol. 46, 1987, pp. 175-185. | Numdam | MR | Zbl
and ,[9] On the Mathematical Description of Quantized Fields, Commun. Math. Phys., Vol. 18, 1970, pp. 291-300. | MR | Zbl
, and ,[10] Local Algebras of Observables and Pointlike Localized Fields, Commun. Math. Phys., Vol. 80, 1981, pp. 555-561. | MR | Zbl
and ,[11] Topological Algebras and their Applications in Quantum Statistics, Wiss. Z. KMU, Leipzig, Math.-Nat. R., Vol. 6, 1981, pp. 572-595. | MR | Zbl
,[12] Algebras of Unbounded Operators and Quantum Dynamics, Physica, Vol. 124A, 1984, pp. 471-480. | Zbl
,[13] Qu *-Algebras and Twisted Product, Publ. RIMS, Kyoto Univ., Vol. 25, 1989, pp. 279-299. | MR | Zbl
and ,[14] Canonical Commutation Relations on the Interval, J. Math. Phys., Vol. 28, 1987, pp. 174-177. | MR | Zbl
, and ,[15] The Completion of the Maximal Op*-Algebra on a Frechet Domain, Publ. RIMS, Kyoto Univ., Vol. 22, 1986, pp. 151-175. | MR | Zbl
,[16] Duality for Maximal Op*-Algebras on Frechet Domains, Publ. RIMS, Kyoto Univ., Vol. 24, 1988, pp. 585-620. | MR | Zbl
,[17] States and Derivations on Quasi *-Algebras, J. Math. Phys., Vol. 29, 1988, pp. 1885-1890. | MR | Zbl
,[18] Partial *-Algebras of Closed Linear Operators in Hilbert Space, Publ. RIMS, Kyoto Univ., Vol. 21, 1985, pp. 205-236. | MR | Zbl
and ,[19] Partial *-Algebras of Closed Operators and their Commutants, I. General Structure, Ann. Inst. Henri Poincaré, Vol. 46, 1987, pp. 299-324. | Numdam | MR | Zbl
and ,[20] Partial *-Algebras of Closed Operators and their Commutants, II. Commutants and Bicommutants, Vol. 46, 1987, pp. 325-351. | Numdam | MR | Zbl
, and ,[21] Partial *-Algebras of Closable Operators, I: The Basic Theory and the Abelian Case, Publ. RIMS, Kyoto Univ., Vol. 26, 1990, pp. 359-395. | MR | Zbl
, and ,[22] Partial *-Algebras of Closable Operators, II: States and Representations of Partial *-Algebras, Publ. RIMS, Kyoto University, Vol. 27, 1991, pp. 399-430. | MR | Zbl
, and ,[23] Unbounded Operator Algebras and Representations Theory, Birkhauser, Basel, 1990. | MR
,[24] Generalized B *-Algebras, Proc. London Math. Soc., Vol. 21, 1970, pp. 693-715. | MR | Zbl
,[25] On a Class of Locally Convex Algebras, Proc. London Math. Soc., Vol. 17, 1967, pp. 91-114. | MR | Zbl
,[26] Lokal Multiplicativ Konvexe Op *-Algebren, Math. Nach., Vol. 85, 1978, pp. 161-170. | MR | Zbl
,[27] V *-Algebras: a Particular Class of Unbounded Operator Algebras, J. Math. Phys., Vol. 25, 1984, p. 2633. | MR | Zbl
and ,[28] Methods of Modern Mathematical Physics, I, Academic Press, New York, 1980. | MR
and ,[29] Characterizations of C*-Algebras, Pure and Applied Mathematics, M. Dekker, Inc., New York, Basel, 1986. | MR | Zbl
and ,[30] Elementary Properties of Nested Hilbert Spaces, Commun. Math. Phys., Vol. 2, 1966, pp. 1-30. | MR | Zbl
,[31] Les C*-algèbres et leurs représentations, Gauthier-Villars, Paris, 1964. | MR | Zbl
,[32] C*-Algebras and W*-Algebras, Springer-Verlag, 1971. | MR | Zbl
,[33] Fundamentals of the Theory of Operator Algebras, I et II, Academic Press, New York, 1983. | MR | Zbl
and ,[34] Operator Algebras and Quantum Statistical Mechanics, I, Springer Verlag, New York, 1979. | MR | Zbl
and ,[35] Spontaneous Symmetry Breakdown and Related Subjects, p. 247; L. MICHEL, J. MOZRZYMAS and A. PEKALSKI, eds., World Scientific, Singapore, 1985. | MR
, in[36] Weights on Partial *-Algebras, Preprint. | MR
, and ,[37] General Theory of Banach Algebras, van Nostrand, Princeton, 1960. | MR | Zbl
,[38] Generalized Functions, IV, Academic Press, New York, 1964.
and ,[39] Bull. Acad. Pol. Sci., Theor. Phys., Vol. XXVII, 1979, p. 223. | MR | Zbl
and ,[40] Some Operator Algebras in Nested Hilbert Spaces, Commun. Math. Phys., Vol. 42, 1975, pp. 183-193. | MR | Zbl
,[41] Partial Inner Product Spaces I, II, J. Funct. Anal., Vol. 23, 1976, pp. 369-378; Vol. 23, 1976, pp. 379-391. | Zbl
and ,[42] Partial Inner Product Spaces. IV. Topological Considerations, J. Math. Phys., Vol. 21, 1980, p. 2067. | MR | Zbl
,[43] Topological Vector Spaces, I, Springer-Verlag, Berlin, New York, 1983. | MR
,[44] 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 | Zbl
,[45] On the Continuity of Entropy, Rep. Math. Phys., Vol. 15, 1975, p. 41. | MR | Zbl
and ,[46] The General Theory of Quantized Fields, American Mathematical Society, Providence, 1965. | MR | Zbl
,[47] Introduction to Algebraic Quantum Field Theory, Kluwer Academic Publishers, Dordrecht, 1990. | MR
,[48] New Generalized Functions and Multiplication of Distributions, North-Holland, Amsterdam, 1984. | MR | Zbl
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