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Large groups of automorphisms of C*-algebras

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Abstract

Groups of *-automorphisms ofC*-algebras and their invariant states are studied. We assume the groups satisfy a certain largeness condition and then obtain results which contain many of those known for asymptotically abelianC*-algebras and for inner automorphisms and traces ofC*-algebras. Our key result is the construction in certain “finite” cases, where the automorphisms are spatial, of an invariant linear map of theC*-algebra onto the fixed point algebra carrying with it most of the relevant information.

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References

  1. Bauer, H.: Konvexität in topologischen Vektorräumen. Universität Hamburg 1964.

  2. Borchers, H. J.: On the vacuum state in quantum field theory. II. Commun. Math. Phys.1, 57–79 (1965).

    Google Scholar 

  3. Choquet, G., etP. A. Meyer: Existence et unicité des représentations intégrales dans les convexes compacts quelconques. Ann. Inst. Fourier, Grenoble13, 139–154 (1963).

    Google Scholar 

  4. Dixmier, J.: Les algèbres d'opérateurs dans l'espace hilbertien. Paris: Gauthier-Villars 1957.

    Google Scholar 

  5. —— LesC*-algèbres et leurs représentations. Paris: Gauthier-Villars 1964.

    Google Scholar 

  6. Doplicher, S.: An algebraic spectrum condition. Commun. Math. Phys.1, 1–5 (1965).

    Google Scholar 

  7. ——D. Kastler, andD. W. Robinson: Covariance algebras in field theory and statistical mechanics. Commun. Math. Phys.3, 1–28 (1966).

    Google Scholar 

  8. Dunford, N., andJ. Schwartz: Linear operators. Part I. New York: Interscience Publishers 1958.

    Google Scholar 

  9. Glimm, J., andR. V. Kadison: Unitary operators inC*-algebras. Pacific J. Math.10, 547–556 (1960).

    Google Scholar 

  10. Haag, R., andD. Kastler: An algebraic approach to quantum field theory. J. Math. Phys.5, 848–861 (1964).

    Google Scholar 

  11. Kadison, R. V.: Transformations of states in operator theory and dynamics. Topology, suppl.2, 177–198 (1965).

    Google Scholar 

  12. —— andJ. R. Ringrose: Derivations and automorphisms of operator algebras. Commun. Math. Phys.4, 32–63 (1967).

    Google Scholar 

  13. Kastler, D., andD. W. Robinson: Invariant states in statistical mechanics. Commun. Math. Phys.3, 151–180 (1966).

    Google Scholar 

  14. Lanford, O., andD. Ruelle: Integral representations of invariant states onB*-algebras. To appear.

  15. Ruelle, D.: States of physical systems. Commun. Math. Phys.3, 133–150 (1966).

    Google Scholar 

  16. Segal, I. E.: A class of operator algebras which are determined by groups. Duke Math. J.18, 221–265 (1951).

    Google Scholar 

  17. Thoma, E.: Über unitäre Darstellungen abzählbarer, diskreter Gruppen. Math. Ann.153, 111–138 (1964).

    Google Scholar 

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Authors and Affiliations

  1. University of Oslo, Oslo, Norway

    Erling Størmer

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  1. Erling Størmer
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Størmer, E. Large groups of automorphisms of C*-algebras. Commun.Math. Phys. 5, 1–22 (1967). https://doi.org/10.1007/BF01646355

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