Extension of representations in quasi * -algebras
Annales de l'I.H.P. Physique théorique, Tome 69 (1998) no. 2, pp. 241-264. 
@article{AIHPA_1998__69_2_241_0,
     author = {Antoine, J.-P. and Bagarello, F. and Trapani, C.},
     title = {Extension of representations in quasi $^\ast $-algebras},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {241--264},
     publisher = {Gauthier-Villars},
     volume = {69},
     number = {2},
     year = {1998},
     mrnumber = {1638895},
     zbl = {0922.46048},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1998__69_2_241_0/}
}
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Antoine, J.-P.; Bagarello, F.; Trapani, C. Extension of representations in quasi $^\ast $-algebras. Annales de l'I.H.P. Physique théorique, Tome 69 (1998) no. 2, pp. 241-264. http://www.numdam.org/item/AIHPA_1998__69_2_241_0/

[1] A. Jaffe and J. Glimm, Quantum Physics, A Functional Integral Point of View, Springer-Verlag, Berlin et al., 1981. | MR | Zbl

[2] O. Bratteli and D. Robinson, Operator Algebras and Quantum Statistical Mechanics I, II, Springer-Verlag, Berlin et al., 1979. | MR

[3] 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 | Zbl

[4] 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

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

[6] 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

[7] F. Bagarello and C. Trapani, 'Almost' mean field Ising model: An algebraic approach, J. Stat. Phys., Vol. 65, 1991, pp. 469-482. | MR | Zbl

[8] F. Bagarello and C. Trapani, A note on the algebraic approach to the almost mean field Heisenberg model, Nuovo Cim., Vol. 108B, 1992, pp. 849-866. | MR

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

[10] 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

[11] 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

[12] C. Trapani, Quasi*-algebras of operators and their applications, Reviews Math. Phys., Vol. 7, 1995, pp. 1303-1332. | MR | Zbl

[13] H.J. Borchers and J. Yngvason, On the algebra of field operators. The weak commutant and integral decompositions of states, Commun. Math. Phys., Vol. 42, 1975, pp. 231-252. | MR | Zbl

[14] I.M. Gelfand and N.Ya. Vilenkin, Generalized Functions, Vol. IV, Academic Press, New York, 1964.

[15] C. Trapani, States and derivations on quasi*-algebras, J. Math. Phys., Vol. 29, 1988, pp. 1885-1890. | MR | Zbl

[16] R.T. Powers, Self-adjoint algebras of unbounded operators, Commun. Math. Phys., Vol. 21, 1971, pp. 85-124. | MR | Zbl

[17] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin et al., 1966. | MR | Zbl

[18] J.-P. Antoine, Y. Soulet and C. Trapani, Weights on partial *-algebras, J. Math. Anal. Appl., Vol. 192, 1995, pp. 920-941. | MR | Zbl

[19] A. Russo and C. Trapani, Quasi*-algebras and multiplication of distributions, J. Math. Anal. Appl., Vol. 215, 1997, pp. 423-442. | MR | Zbl

[20] F. Bagarello and C. Trapani, Lp-spaces as quasi*-algebras, J. Math. Anal. Appl., Vol. 197, 1996, pp. 810-824. | MR | Zbl