Perturbations and ground states of $C^ \ast$-dynamical systems
HTML articles powered by AMS MathViewer
- by Hideki Kurose PDF
- Proc. Amer. Math. Soc. 95 (1985), 242-246 Request permission
Abstract:
In this paper we show that if a ${C^ * }$-dynamical system has an irreducible covariant representation, every relatively bounded $*$-derivation for its generator is also implemented by a relatively bounded selfadjoint operator for that associated with the dynamics. As its application, we assert that the existence of ground states of a ${C^ * }$-dynamical system is stable under sufficiently small perturbations.References
- Huzihiro Araki, Relative Hamiltonian for faithful normal states of a von Neumann algebra, Publ. Res. Inst. Math. Sci. 9 (1973/74), 165–209. MR 0342080, DOI 10.2977/prims/1195192744
- C. J. K. Batty, Small perturbations of $C^{\ast }$-dynamical systems, Comm. Math. Phys. 68 (1979), no. 1, 39–43. MR 539735, DOI 10.1007/BF01562540
- C. J. K. Batty, Perturbations of ground states of type $\textrm {I}$ $C^{\ast }$-algebras, Proc. Amer. Math. Soc. 78 (1980), no. 4, 539–544. MR 556628, DOI 10.1090/S0002-9939-1980-0556628-9
- Ola Bratteli, Frederick M. Goodman, and Palle E. T. Jorgensen, Unbounded derivations tangential to compact groups of automorphisms. II, J. Funct. Anal. 61 (1985), no. 3, 247–294. With a comment by Klaus Thomsen. MR 820616, DOI 10.1016/0022-1236(85)90022-9
- Ola Bratteli and Derek W. Robinson, Unbounded derivations of $C^{\ast }$-algebras, Comm. Math. Phys. 42 (1975), 253–268. MR 377526, DOI 10.1007/BF01608976 —, Operator algebras and quantum statistical mechanics. I, II, Springer-Verlag, Berlin and New York, 1979, 1981.
- Frederick M. Goodman and Palle E. T. Jorgensen, Lie algebras of unbounded derivations, J. Funct. Anal. 52 (1983), no. 3, 369–384. MR 712587, DOI 10.1016/0022-1236(83)90075-7
- Akitaka Kishimoto, Derivations with a domain condition, Yokohama Math. J. 32 (1984), no. 1-2, 215–223. MR 772917
- Roberto Longo, Automatic relative boundedness of derivations in $C^{\ast }$-algebras, J. Functional Analysis 34 (1979), no. 1, 21–28. MR 551107, DOI 10.1016/0022-1236(79)90022-3
- Michael Reed and Barry Simon, Methods of modern mathematical physics. I, 2nd ed., Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1980. Functional analysis. MR 751959 S. Sakai, The theory of unbounded derivations in ${C^*}$-algebras, Univ. of Copenhagen and Newcastleupon-Tyne, Lecture Notes, 1977.
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 95 (1985), 242-246
- MSC: Primary 46L55; Secondary 46L40
- DOI: https://doi.org/10.1090/S0002-9939-1985-0801331-5
- MathSciNet review: 801331