Unbounded representations of a *-algebra on indefinite metric space
Ôta, Schôichi
Annales de l'I.H.P. Physique théorique, Tome 49 (1988), p. 333-353 / Harvested from Numdam
Publié le : 1988-01-01
@article{AIHPA_1988__48_4_333_0,
     author = {\^Ota, Sch\^oichi},
     title = {Unbounded representations of a $\ast $-algebra on indefinite metric space},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {49},
     year = {1988},
     pages = {333-353},
     mrnumber = {969171},
     zbl = {0673.46034},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1988__48_4_333_0}
}
Ôta, Schôichi. Unbounded representations of a $\ast $-algebra on indefinite metric space. Annales de l'I.H.P. Physique théorique, Tome 49 (1988) pp. 333-353. http://gdmltest.u-ga.fr/item/AIHPA_1988__48_4_333_0/

[1] T. Ando, Linear operators on Krein spaces. Lectures Note in Hokkaido Univ., 1979. | MR 560903 | Zbl 0429.47016

[2] J. Bognar, Indefinite inner product spaces. Berlin, Springer Verlag, 1974. | MR 467261 | Zbl 0286.46028

[3] H.J. Borchers, Algebraic aspects of Wighttman field theory in Statistical Mechanics and Field Theory Lectures, 1971, New York, Jerusalem, London, 1972. | Zbl 0264.46061

[4] H.J. Borchers and J. Yungvason, Commun. Math. Phys., t. 42, 1975, p. 231-252. | MR 377550 | Zbl 0307.46053

[5] Yu. Dadashyan and S.S. Khoruzhii, Theor. Math. Phys., t. 54, 1983, p. 35-48. | Zbl 0536.47035

[6] O. Bratteli and D.W. Robinson, Operator algebras and quantum statistical mechanics, Berlin, Springer Verlag, 1979. | MR 545651 | Zbl 0421.46048

[7] S. Gudder and W. Scruggs, Pacific J. Math., t. 70, 1977, p. 369-382. | MR 482269 | Zbl 0374.46045

[8] U. Haagerup, Ann. Math., t. 118, 1983, p. 215-224. | MR 717823 | Zbl 0543.46033

[9] A. Inoue and K. Takesue, Trans. Amer. Math., t. 280, 1983, p. 393-400. | MR 712267 | Zbl 0529.47038

[10] I.S. Iohividov, M.G. Krein and H. Langer, Introduction to the spectral theory of operators in spaces with indefinite metric, Berlin, Akademie Verlag, 1982. | MR 691137 | Zbl 0506.47022

[11] A.Z. Jadczyk, Rep. Math. Phys., t. 2, 1971, p. 263-276. | Zbl 0228.47018

[12] L. Jakobczyk, J. Math. Phys., t. 25, 1984, p. 617-622. | MR 737311

[13] L. Jakobczyk, Ann. Phys., t. 161, 1985, p. 314-336. | MR 793818 | Zbl 0579.46015

[14] G. Lassner, Rep. Math. Phys., t. 3, 1972, p. 270-293. | Zbl 0252.46087

[15] N.A. Naimark, Linear representations of the Lorentz groups, London, Pergamon, 1964.

[16] S. Ôta, Acta Sci. Math. (Szeged), t. 39, 1977, p. 129-133. | MR 440377 | Zbl 0345.46045

[17] S. Ôta, J. Funct. Anal., t. 30, 1978, p. 238-244. | MR 515227 | Zbl 0388.46040

[18] S. Ôta, J. Reine Angew. Math., t. 347, 1984, p. 21-32. | MR 733045 | Zbl 0516.46042

[19] R.S. Phillips, The extension of dual subspaces invariant under algebra. Proc. Inter. Symp. On Linear Spaces. Jerusalem, 1960, p. 366-398. | MR 133686 | Zbl 0115.33003

[20] R.T. Powers, Commun. Math. Phys., t. 21, 1971, p. 85-124. | MR 283580 | Zbl 0214.14102

[21] R.T. Powers, Trans. Amer. Math. Soc., t. 187, 1974, p. 261-293. | MR 333743 | Zbl 0296.46059

[22] S. Sakai, C*-algebras and W*-algebras, Berlin, Springer Verlag, 1971. | MR 1490835 | Zbl 0219.46042

[23] K. Schmüdgen, Publ. R. I. M. S. (Kyoto), t. 19, 1983, p. 601-671. | MR 716970 | Zbl 0557.47023

[24] A.N. Vasl'Ev, Theor. Math. Phys., t. 2, 1970, p. 113-123.

[25] A.H. Völkel, J. Math. Phys., t. 26, 1985, p. 2956-2973. | MR 808512 | Zbl 0582.22018

[26] A.H. Völkel, J. Math. Phys., t. 27, 1986, p. 1113-1127. | MR 832798 | Zbl 0592.22018

[27] G. Warner, Harmonic analysis on semi-simple Lie groups I, Berlin, Springer Verlag, 1972. | MR 498999 | Zbl 0265.22020