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Inner limit derivations
Author:
Richard H. Herman
Journal:
Proc. Amer. Math. Soc. 76 (1979), 113-116
MSC:
Primary 46L10
MathSciNet review:
534399
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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.
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Ola
Bratteli and Uffe
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Bratteli and Derek
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W. Robinson, Unbounded derivations and invariant trace states,
Comm. Math. Phys. 46 (1976), no. 1, 31–35. MR 0405122
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Connes and Erling
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𝐼𝐼𝐼₁, J. Functional Analysis
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(57 #10435)
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no. 2, 113–129. MR 0468992
(57 #8793)
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- [1]
- O. Bratteli and U. Haagerup, Unbounded derivations and invariant states, Comm. Math. Phys. 59 (1978), 79-95. MR 0482251 (58:2329)
- [2]
- O. Bratteli and D. W. Robinson, Unbounded derivations of von Neumann algebras, Ann. Inst. H. Poincaré Sect. A (N.S.) 25 (1976), 139-164. MR 0425632 (54:13586)
- [3]
- -, Unbounded derivations and invariant trace states, Comm. Math. Phys. 46 (1976), 31-35. MR 0405122 (53:8917)
- [4]
- A. Connes and E. Størmer, Homogeneity of the state space of factors of type III, J. Functional Analysis 28 (1978), 187-196. MR 0470689 (57:10435)
- [5]
- T. Kato, Perturbation theory for linear operators, Springer-Verlag, New York, 1966. MR 0203473 (34:3324)
- [6]
- C. Marchioro, A. Pellegrinotti and M. Pulvirenti, Self-adjointness of the Liouville operator for infinite classical systems, Comm. Math. Phys. 58 (1978), 113-129. MR 0468992 (57:8793)
- [7]
- R. T. Powers, Resistance inequalities for KMS states of the isotropic Heisenberg model, Comm. Math. Phys. 51 (1976), 151-156. MR 0426743 (54:14680)
- [8]
- R. T. Powers and S. Sakai, Unbounded derivations in operator algebras, J. Functional Analysis 19 (1975), 81-95. MR 0383093 (52:3974)
- [9]
- M. Takesaki, Tomita's theory of modular Hilbert algebras and its applications, Lecture Notes in Math., vol. 128, Springer-Verlag, Berlin and New York, 1970. MR 0270168 (42:5061)
- [10]
- S. Banach and S. Saks, Sur la convergence forte dans les champs
 , Studia Math. 2 (1930), 51-57. MR 0029381 (10:590g)
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DOI:
http://dx.doi.org/10.1090/S0002-9939-1979-0534399-1
PII:
S 0002-9939(1979)0534399-1
Article copyright:
© Copyright 1979 American Mathematical Society
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