Inner limit derivations

Herman, Richard H.

doi:10.1090/S0002-9939-1979-0534399-1

Inner limit derivations
HTML articles powered by AMS MathViewer

by Richard H. Herman PDF

Proc. Amer. Math. Soc. 76 (1979), 113-116 Request permission

Abstract:

We give a condition involving the approximating derivations and a faithful state which, in conjunction with the “core condition", guarantees that the derivation gives rise to an automorphism group of the von Neumann algebra coming from the state via the GNS procedure.

References

Ola Bratteli and Uffe Haagerup, Unbounded derivations and invariant states, Comm. Math. Phys. 59 (1978), no. 1, 79–95. MR 482251
Ola Bratteli and Derek W. Robinson, Unbounded derivations of von Neumann algebras, Ann. Inst. H. Poincaré Sect. A (N.S.) 25 (1976), no. 2, 139–164. MR 425632
Ola Bratteli and Derek W. Robinson, Unbounded derivations and invariant trace states, Comm. Math. Phys. 46 (1976), no. 1, 31–35. MR 405122
Alain Connes and Erling Størmer, Homogeneity of the state space of factors of type $\textrm {III}_{1}$, J. Functional Analysis 28 (1978), no. 2, 187–196. MR 0470689, DOI 10.1016/0022-1236(78)90085-x
Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
C. Marchioro, A. Pellegrinotti, and M. Pulvirenti, Selfadjointness of the Liouville operator for infinite classical systems, Comm. Math. Phys. 58 (1978), no. 2, 113–129. MR 468992
Robert T. Powers, Resistance inequalities for KMS states of the isotropic Heisenberg model, Comm. Math. Phys. 51 (1976), no. 2, 151–156. MR 426743
Robert T. Powers and Shôichirô Sakai, Unbounded derivations in operator algebras, J. Functional Analysis 19 (1975), 81–95. MR 0383093, DOI 10.1016/0022-1236(75)90007-5
M. Takesaki, Tomita’s theory of modular Hilbert algebras and its applications, Lecture Notes in Mathematics, Vol. 128, Springer-Verlag, Berlin-New York, 1970. MR 0270168
S. Banach, Remarques sur les groupes et les corps métriques, Studia Math. 10 (1948), 178–181 (French). MR 29381, DOI 10.4064/sm-10-1-178-181