Commuting normal operators in partial L 2 (ℝ 2 )-algebras
Antoine, J.-P. ; Karwowski, W.
Annales de l'I.H.P. Physique théorique, Tome 51 (1989), p. 161-185 / Harvested from Numdam
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@article{AIHPA_1989__50_2_161_0,
     author = {Antoine, J.-P. and Karwowski, W.},
     title = {Commuting normal operators in partial $L^2 (\mathbb {R}^2)$-algebras},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {51},
     year = {1989},
     pages = {161-185},
     mrnumber = {1002818},
     zbl = {0678.47041},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1989__50_2_161_0}
}

Antoine, J.-P.; Karwowski, W. Commuting normal operators in partial $L^2 (\mathbb {R}^2)$-algebras. Annales de l'I.H.P. Physique théorique, Tome 51 (1989) pp. 161-185. http://gdmltest.u-ga.fr/item/AIHPA_1989__50_2_161_0/

[1] R.T. Powers, Commun. Math. Phys., t. 21, 1971, p. 85 ; Trans. Amer. Math. Soc., t. 187, 1974, p. 261. | MR 283580 | Zbl 0214.14102

[2] G. Lassner, Reports Math. Phys., t. 3, 1972, p. 279 ; Wiss. Z. Karl-Marx-Univ. Leipzig, Math.-Naturwiss. R., t. 24, 1975, p. 465 ; t. 30, 1981, p. 572. | MR 322527 | Zbl 0252.46087

[3] J.-P. Antoine and W. Karwowski, Publ. RIMS, Kyoto Univ., t. 21, 1985, p. 205; Add. ibid., t. 22, 1986, p. 507. | MR 861779 | Zbl 0609.47058

[4] J.-P. Antoine and F. Mathot, Ann. Inst. H. Poincaré, t. 46, 1987, p. 299. | Numdam | MR 892367 | Zbl 0629.46048

[5] J.-P. Antoine and G. Lassner, Representations of partial *-algebras and sesquilinear forms (unpublished).

[6] J.-P. Antoine, In: Spontaneous Symmetry Breakdown and Related Topics (Karpacz, 1985), p. 247-267 ; L. Michel, J. Mozrzymas and A. Pekalski (eds.) ; World Scientific, Singapore, 1985. | MR 835511

[7] J.-P. Antoine, F. Mathot and C. Trapani, Ann. Inst. H. Poincaré, t. 46, 1987, p. 325. | Numdam | MR 892368 | Zbl 0629.46049

[8] G. Epifanio and C. Trapani, J. Math. Phys., t. 25, 1984, p. 2633. | MR 756559 | Zbl 0556.47026

[9] E. Nelson, Ann. Math., t. 70, 1959, p. 572. | MR 107176 | Zbl 0091.10704

[10] M. Reed and B. Simon, Methods of Modern Mathematical Physics. I. Functional Analysis. II. Fourier Analysis, Self-adjointness, Academic, New York, 1972, 1975 . | MR 493419 | Zbl 0242.46001

[11] K. Schmüdgen, Acta Sci. Math. (Szeged), t. 47, 1984, p. 131 ; Manuscr. Math., t. 57, 1985, p. 221 ; Math. Nachr., t. 125, 1986, p. 83. K. Schmüdgen and J. Friedrich, J. Int. Eq. and Oper. Th., t. 7, 1984, p. 815. | Zbl 0576.47014

[12] P.E.T. Jörgensen and R.T. Moore, Operator Commutation Relations, Reidel, Dordrecht and Boston, 1984. P.E.T. Jörgensen, J. Math. Anal. Appl., t. 123, 1987, p. 508. | MR 746138 | Zbl 0626.47042

[13] J.-P. Antoine, G. Epifanio and C. Trapani, Helv. Phys. Acta, t. 56, 1983, p. 1175. | MR 734580

[14] J.-P. Antoine, A. Inoue and C. Trapani, Partial *-algebras of closable operators. I. The general theory and the abelian case, preprint UCL-IPT-88-25 (to be published).

[15] J. Roberts, J. Math. Phys., t. 7, 1966, p. 1097 ; Commun. Math. Phys., t. 3, 1966, p. 98. | MR 216836 | Zbl 0144.23404

[16] A. Böhm. Boulder Lectures in Theoretical Physics, t. 9A, 1966, p. 255 ; The Rigged Hilbert Space and Quantum Mechanics, Lecture Notes in Physics, t. 78, Springer, Berlin, 1978. | Zbl 0388.46045

[17] J.-P. Antoine, J. Math. Phys., t. 10, 1969, p. 53 et 2276. | Zbl 0172.56602

[18] F. Riesz and B. Sz. Nagy, Leçons d'Analyse Fonctionnelle, Gauthier-Villars, Paris and Akadémiai Kiado, Budapest, 1968.

[19] N.I. Akhiezer and I.M. Glazman, Theory of Linear Operators in Hilbert Spaces, I, II. F. Ungar, New York, 1966. | Zbl 0098.30702

[20] J. Weidmann, Linear Operators in Hilbert Spaces, Springer, Berlin, 1980. | MR 566954 | Zbl 0434.47001

[21] I.M. Gelfand and N.Y. Vilenkin, Les Distributions, t. 4, Dunod, Paris, 1967. | Zbl 0179.18502

[22] J.M. Jauch and B. Misra, Helv. Phys. Acta, t. 38, 1965, p. 30. | MR 209878 | Zbl 0138.43703

[23] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien (algèbres de von Neumann), Gauthier-Villars, Paris, 1957. | MR 94722 | Zbl 0088.32304

[24] O.A. Nielsen, Direct Integral Theory, Marcel Dekker, New York, 1980. | MR 591683 | Zbl 0482.46037

[25] J.-P. Antoine, A. Inoue and C. Trapani, Partial *-algebras of closable operators. II-IV (in preparation).

[26] C.R. Putnam, Commutation Properties of Hilbert Space Operators and Related Topics, Springer, Berlin, 1967. | Zbl 0149.35104

[27] F. Mathot, J. Math. Phys., t. 26, 1985, p. 1118. | MR 790044 | Zbl 0614.47034

[28] W.G. Faris, Self-Adjoint Operators, Lect. Notes Math., t. 433, Springer, Berlin, 1975. | MR 467348 | Zbl 0317.47016

[29] P.R. Halmos, Measure Theory, Van Nostrand, Princeton, 1950. | MR 33869 | Zbl 0040.16802

[30] P.R. Halmos, Naive Set Theory, Van Nostrand, Princeton, 1961. | MR 114756 | Zbl 0087.04403