Abstract
We consider the set of pure states of aC*-algebra as a uniform space equipped with transition probabilities and orientation, and show that the pure states with this structure determine theC*-algebra up to *-isomorphism.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Akemann, C. A.: J. Funct. Anal.4, 277–294 (1969)
Akemann, C. A.: J. Funct. Anal.305–317 (1970)
Alfsen, E. M.: In Ergebnisse der Mathematik, Vol.57, Berlin: Springer 1971
Alfsen, E. M., Shultz, F. W.: Acta Math.140, 155–190 (1978)
Alfsen, E. M., Hanche-Olsen, H., Shultz, F. W.: State spaces ofC*-algebras. Acta Math. (to appear)
Dixmier, J.:C*-algebras. Amsterdam: North-Holland Publ. Co. 1977
Fell, J. M. G.: Ill. J. Math.4, 221–230 (1960)
Effros, E. G.: Injectives and tensor products for convex sets andC*-algebras. Proceedings of NATO Conference, Univ. Coll. Swansea, Wales, 1972
Giles, R., Kummer, H.: Indiana Univ. Math. J.21, 91–102 (1971)
Glimm, J.: Ann. Math.73, 572–612 (1961)
Glimm, J.: Ann. Math.72, 216–244 (1960)
Kadison, R. V.: Memoirs A. M. S. 7, (1951)
Kadison, R. V.: Ann. Math.56, 494–503 (1952)
Kadison, R. V.: Topology3, Suppl. 2 177–198 (1965)
Kadison, R. V.: Ann. Math.54, 325–338 (1951)
Kaplansky, I.: Trans. Am. Math. Soc.70, 219–255 (1951)
Sakai, S.: Tokoku Math. J.22, 191–199 (1970)
Shultz, F. W.: Dual maps of Jordan homomorphisms and *-homomorphisms betweenC*-algebras. Pac. J. Math. (to appear)
Wigner, E.: Gruppentheorie und ihre Anwendung. Braunschweig: Vieweg 1931. English transl. by J. J. Griffin, New York: Academic Press 1959.
Author information
Authors and Affiliations
Additional information
Communicated by H. Araki.
Partially supported by NSF grant MCS78-02455
Rights and permissions
About this article
Cite this article
Shultz, F.W. Pure states as a dual object forC*-algebras. Commun.Math. Phys. 82, 497–509 (1982). https://doi.org/10.1007/BF01961237
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01961237