Pacific Journal of Mathematics

Derivations of $C^\ast$-algebras and almost Hermitian representations on $\Pi_k$-spaces.

Edward Kissin, Aleksei I. Loginov, and Viktor S. Shulman
Source: Pacific J. Math. Volume 174, Number 2 (1996), 411-430.
First Page: Show Hide
Primary Subjects: 46L57
Secondary Subjects: 47B47, 47B50, 47D25
Full-text: Open access
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pjm/1102365177
Zentralblatt MATH identifier: 0860.46044
Mathematical Reviews number (MathSciNet): MR1405594

References

[1] H.Araki, Indecomposable Reprentations with Invariant Inner Product,Commun. Math. Phys., 97 (1985), 149-159.
Mathematical Reviews (MathSciNet): MR86f:22023
Zentralblatt MATH: 0582.22017
[2] W.Arveson, Continuous analoguesofFockspace, Mem. of AMS, 80(409) (1989).
Mathematical Reviews (MathSciNet): MR90f:47061
Zentralblatt MATH: 0697.46035
[3] B.A. Barnes, Density theorem for algebrasof operators andannihilator Banach algebras, Michigan Math. J.,19 (1972), 149-155.
Mathematical Reviews (MathSciNet): MR46:6058
Zentralblatt MATH: 0233.46067
[4] K. Bleuler, Eine neue Methode zur Behandlung der longitudinalen und skalaren Photonen, Helv. Phys. Acta, 23 (1950), 567-586.
Mathematical Reviews (MathSciNet): MR12:465h
Zentralblatt MATH: 0040.42404
[5] O. Bratteli and D.W. Robinson, Unbounded derivations of C*-algebras, I, Comm. Math. Phys., 42 (1975), 253-268.
Mathematical Reviews (MathSciNet): MR51:13698
Zentralblatt MATH: 0344.46118
[6] J. Cuntz, Locally C*-equivalent algebras,J. Funct. Anal., 23 (1976), 95-106.
Mathematical Reviews (MathSciNet): MR56:6398
Zentralblatt MATH: 0343.46038
[7] M Flato and C. Fronsdal, Quantum field theory of singletons, J. Math. Phys., 22 (1981), 1100-1105.
Mathematical Reviews (MathSciNet): MR82j:81048
[8] I.M. Gelfand, M.L Graev and N.Ya. Vilenkin, Integral geometry and related prob- lems of representation theory, FizMatgiz, Moskow, 1962.
[9] I.M. Gelfand and A.M. Yaglom, General relativistic invariant equations and infinite dimensional representations of the Lorentz group, J. Exp. Th. Ph., 18 (1948), 703- 733.
[10] S.N. Gupta, Theory of longitudinal photons in quantum electrodynamics, Proc. Phys. Soc, 63 (1950), 681-691.
Mathematical Reviews (MathSciNet): MR12:67h
Zentralblatt MATH: 0040.42403
[11] R.S. Ismagilov, Rings of operators in a space with an indefinite metric, Dokl. Acad. Nauk SSSR, 2 (1966)= Soviet Math. Dokl., 7(6) (1966), 1460-1462.
Zentralblatt MATH: 0162.18801
[12] R.S. Ismagilov, Unitary representations of the Lorentz group in spaces with indefinite met- ric, Izv. Akad. Nauk SSSR, 3 (1966), 497-522.
Mathematical Reviews (MathSciNet): MR34:1451
[13] R.S. Ismagilov, On the problem of extension of representations, Matem. Zametki, 35(1) (1984), 99-105.
Mathematical Reviews (MathSciNet): MR85e:22008
[14] B.E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc, 127 (1972).
Mathematical Reviews (MathSciNet): MR51:11130
Zentralblatt MATH: 0256.18014
[15] P.E.T. Jorgensen and P.S. Muhly, Self adjoint extensions satisfying the Weyl oper- ator commutation relations, J. Analyse Math., 37 (1980), 46-99.
[16] P.E.T. Jorgensen and G.L. Price, Index theory and second quantization of boundary value problems, J. Funct. Anal., 104 (1992), 243-290.
Mathematical Reviews (MathSciNet): MR93i:46121
Zentralblatt MATH: 0788.47025
[17] E.V. Kissin, Symmetric operator extensions of unbounded derivations of C*-algebras, J. Funct. Anal., 81 (1988), 38-53.
Mathematical Reviews (MathSciNet): MR89k:46076
Zentralblatt MATH: 0668.46032
[18] E.V. Kissin, Dissipative implementations of *-derivations of C*-algebras and represen- tations in indefinite metric spaces, J. London Math. Soc, 43 (1991), 451-464.
Mathematical Reviews (MathSciNet): MR92j:46121
Zentralblatt MATH: 0747.46047
[19] E.V. Kissin, Indices of unbounded derivations of C*-algebras,Pac J. Math., 152 (1992), 125-150.
Mathematical Reviews (MathSciNet): MR93a:46134
Zentralblatt MATH: 0713.47037
[20] E.V. Kissin, Representational indices of derivations of C*-algebras and representations of ^-algebras on Krein spaces, J. reine angew. Math., 439 (1993), 71-92.
Mathematical Reviews (MathSciNet): MR94h:46102
[21] E.V. Kissin, On the uniqueness of representational indices of derivations of C* -algebras, Pac J. Math., 162 (1994), 97-120.
Mathematical Reviews (MathSciNet): MR94k:46145
Zentralblatt MATH: 0792.46050
[22] E.V. Kissin and V.S. Shulman, Dense Q-subalgebrasof Banach and C*-algebrasand unbounded derivations of Banach and C*-algebras, Proceedings of the Edinburgh Math. Soc, 36 (1993), 261-276.
Zentralblatt MATH: 0792.46041
[23] M.G. Krein, Introduction to the geometry of indefinite J-spaces and to the theory of operators in those spaces, Amer. Math. Soc Transl., 93 (1970), 103-176.
Zentralblatt MATH: 0206.11906
[24] A.I. Loginov and V.S. Shulman, Irreducible J-symmetric algebras of operators in spaces with an indefinite metric, Dokl. Akad. Nauk SSSR, 240 (1) (1978)= Soviet Math. Dokl., 19(3) (1978), 541-544.
Zentralblatt MATH: 0415.47017
[25] A.I. Loginov and V.S. Shulman, Invariant subspaces of operator algebras,Mat. Anal. (Itogi Nauki. VINITI
Zentralblatt MATH: 0725.47005
[26] G. Morchio, D. Pierotti and F. Strocchi, Infrared and vacuum structurein two- dimensional quantum field theory models. The massless scalar field, J. Math. Phys., 31 (1990), 1467-1477.
Mathematical Reviews (MathSciNet): MR91f:81087
Zentralblatt MATH: 0712.46044
[27] M.A. Naimark, Linear representationsof the Lorentz group, Fizmatgiz, 1958.
Mathematical Reviews (MathSciNet): MR21:4995
[28] M.A. Naimark, On commuting unitary operators in spaces with indefinite metric, Acta Sci. Math., 24 (1963), 177-189.
Mathematical Reviews (MathSciNet): MR28:4367
Zentralblatt MATH: 0115.33301
[29] M.A. Naimark and R.S. Ismagilov, Representationsof groups and algebras in spaces with indefinite metric, Mat. Anal. 1968. (Itogi Nauki. VINITI Akad. Nauk SSSR), Moscow, (1969), 73-105.
Mathematical Reviews (MathSciNet): MR54:3424
Zentralblatt MATH: 0239.47030
[30] M.A. Naimark,A.I. Loginov and V.S. Shulman, Non-self adjoint operator algebras in Hubert spaces, Mat. Anal. (Itogi Nauki. VINITI Akad. Nauk SSSR), 12, 413-465, Moscow, 1974 = J. Soviet Math., 5(2) (1976), 250-278.
[31] H. Nakazato, Indefinite inner product spaces and derivations, Math. Japonica, 35 (1990), 1119-1124.
Mathematical Reviews (MathSciNet): MR91m:47049
Zentralblatt MATH: 0726.47025
[32] J.D. Newburgh, The variation of spectra, Duke Math. J., 18 (1951), 165-176.
Mathematical Reviews (MathSciNet): MR14:481b
Zentralblatt MATH: 0042.12302
[33] S. Ota, Certain operator algebras induced by *-derivations in C*-algebras on an indefinite inner product space, J. Funct. Anal., 30 (1978), 238-244.
Mathematical Reviews (MathSciNet): MR80g:46051
Zentralblatt MATH: 0388.46040
[34] R.S. Phillips, Dissipativeoperators and hyperbolic systems of partialdifferential equations, Trans. Amer. Math. Soc, 90 (1959), 193-254.
Mathematical Reviews (MathSciNet): MR21:3669
[35] R.S. Phillips, The extension of dual subspaces invariant under an algebra, Proc.of the International symposium on Linear Spaces (Jerusalem 1960) (Academic Press, Jerusalem, 1961), 366-398.
Mathematical Reviews (MathSciNet): MR24:A3512
Zentralblatt MATH: 0115.33003
[36] R.S. Phillips, On dissipative operators, Lecture series in differential equations, Vol II, Mathematics Studies 19 (ed. A.K. Aziz; von Nostrand, New York, 1969).
Zentralblatt MATH: 0181.15301
[37] R.T. Powers, An index theory for semigroups of *-endomorphisms of B(H) and type Hi factors, Canad. J. Math., XL (1988), 86-114.
Mathematical Reviews (MathSciNet): MR89f:46116
Zentralblatt MATH: 0632.46058
[38] R.T. Powers and D.W. Robinson, An index for continuous semigroups of B(H), J. Funct. Anal., 84 (1989), 85-96.
Mathematical Reviews (MathSciNet): MR90f:46107
Zentralblatt MATH: 0687.47035
[39] J. Rawnsley, W. Schmid and J.A. Wolf, Singular unitary representationsand indef- inite harmonic theory, J. Funct. Anal., 51 (1983), 1-114.
Mathematical Reviews (MathSciNet): MR84j:22022
Zentralblatt MATH: 0511.22005
[40] V.S. Shulman, On representationsof C* -algebras on indefinite metric spaces, Mat. Zametki, 22 (1977), 583-592 = Math. Notes, 22 (1977).
[41] V.S. Shulman, Symmetric Banach algebras of operators in a space of type i, Mat. Sbornik, 89(131) (1972), No 2 = Math. USSR Sbornik, 18(2) (1972), 267-283.
[42] V.S. Shulman, On fixed points of linear-fractional transformations,Funct. Analis i ego prilogenia, 14 (1980), 93-94.
Zentralblatt MATH: 0459.47027
[43] H. Weyl, The theory of groups and quantum mechanics, Dover, New York, 1950.
Zentralblatt MATH: 0041.56804
[44] D.P. Zhelobenko, Description of a certain class of representationsof the Lorentz group, Dokl. Akad. Nauk SSSR, 4 (1958), 586-590.
Mathematical Reviews (MathSciNet): MR21:2920

2013 © Pacific Journal of Mathematics

Pacific Journal of Mathematics

Pacific Journal of Mathematics

Turn MathJax Off
What is MathJax?