Abstract
It is first shown that a *-automorphism of a factor is inner if and only if it is asymptotically equal to the identity automorphism. Then it is shown that a periodic *-automorphism of a von Neumann algebra ℛ is inner if and only if its fixed point algebra is a normal subalgebra of ℛ.
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References
Borchers, H.J.: Characterization of inner *-automorphisms ofW*-algebras, to appear
Christensen, E.: Perturbations of type I von Neumann algebras, to appear
Connes, A.: Une classification des facteurs de type III, Ann. Scient. École Normale Supérieure,4, 133–252 (1973)
Dixmier, J.: Les algèbres d'opérateurs dans l'espace hilbertien. Paris: Gauthier-Villars 1957
Kadison, R., Kastler, D.: Perturbations of von Neumann algebras I. Stability of type. Amer. J. Math.94, 38–54 (1972)
Kadison, R., Ringrose, J.: Derivations and automorphisms of operator algebras. Commun. math. Phys.4, 32–63 (1967)
Lance, E.C.: Inner automorphisms of UHF-algebras. J. London Math. Soc.43, 681–688 (1968)
Størmer, E.: Spectra of ergodic transformations. J. Functional Anal., to appear
Dell' Antonio, G.: Commun. math. Phys.2, 384–397 (1966)
Elliott, G.: On derivations ofA W*-algebras, to appear
Suzuki, N.: Tôhoku Math. J.7, 186–191 (1955)
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Communicated by H. Araki
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Størmer, E. Inner automorphisms of von Neumann algebras. Commun.Math. Phys. 36, 115–122 (1974). https://doi.org/10.1007/BF01646325
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DOI: https://doi.org/10.1007/BF01646325