Advertisement

Positive linear maps of Cu*-algebras

  • Erling Størmer
Course Mathematics
Part of the Lecture Notes in Physics book series (LNP, volume 29)

Keywords

Hilbert Space Pure State Unitary Operator Operator Algebra Jordan Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arveson, W.: Analyticity in operator algebras, Amer.J.Math. 89, 578–642 (1967).Google Scholar
  2. 2.
    :: Subalgebras of C*-algebras, Acta math. 123, 141–224 (1969).Google Scholar
  3. 3.
    : Subalgebras of Cu*-algebras, II, Acta math. 128, 271–308 (1972).Google Scholar
  4. 4.
    ": On groups of automorphisms of operator algebras, To appear.Google Scholar
  5. 5.
    Bendat, J. and Sherman, S.: Monotone and convex operator functions, Trans.Amer.Math.Soc. 79, 58–71 (1955).Google Scholar
  6. 6.
    Borchers, H.J.: On the vacuum state in quantum field theory, II, Commun.math.Phys. 1, 57–79 (1965).CrossRefGoogle Scholar
  7. 7.
    Broise, M.: Une caractérisation des représentations unitaires, Bull.Sc.math. 2 ser., 59–64 (1964).Google Scholar
  8. 8.
    : Une caractérisation des représentations unitaires de certains semi-groups, Bull.Sc.math. 2 ser., 69–79 (1966).Google Scholar
  9. 9.
    : Sur certaines applications unitaires de l'espace des opérateurs de Hilbert-Schmidt, C.R.Acad.Sc.Paris, 263, 722–725 (1966).Google Scholar
  10. 10.
    : Sur les isomorphismes de certaines algébres de von Neumann, Ann.scient, Ec.Norm.Sup. 83, 91–111 (1966).Google Scholar
  11. 11.
    Choi, M.D.: Positive linear maps on C*-algebras, Canad.J.Math. 24, 520–529 (1972).Google Scholar
  12. 12.
    ": Positive linear maps on C*-algebras, Thesis, University of Toronto (1972).Google Scholar
  13. 13.
    Civin, P. and Yood, B.: Lie and Jordan structures in Banach algebras, Pacific J.Math. 15, 775–797 (1965).Google Scholar
  14. 14.
    Connes, A.: Thése, To appear.Google Scholar
  15. 15.
    Davis, C.: A Schwarz inequality for convex operator functions, Proc.Amer.Math.Soc. 8, 42–44 (1957).Google Scholar
  16. 16.
    ": Notions generalizing convexity for functions defined on spaces of matrices, Amer.Math.Soc., Proc. of Symposia in Pure Math. Providence, vol. 7, Convexity 187–201 (1962).Google Scholar
  17. 17.
    Dixmier, J.: Les algébres d'opérateurs dans l'espaces hilbertien, Paris. Gauthier-Villars, 2. ed. (1969).Google Scholar
  18. 18.
    ": Les C*-algébres et leurs représentations. Paris. Gauthier-Villars, (1964).Google Scholar
  19. 19.
    Doplicher, S., Kadison, R., Kastler, D. and Robinson, D.W.: Asymptotically abelian systems. Commun.math.Phys. 6, 101–120 (1967).CrossRefGoogle Scholar
  20. 20.
    Doplicher, S., Kastler, D. and Stormer, E.: Invariant states and asymptotic abelianness, J.Fnal.Anal. 3, 419–434 (1969).CrossRefGoogle Scholar
  21. 21.
    Effros, E.: Order ideals in a C*-algebra and its dual. Duke Math. J. 30, 391–412 (1963).CrossRefGoogle Scholar
  22. 22.
    Gardner, L.T.: On isomorphisms of C*-algebras, Amer.J.Math. 87, 384–396 (1965).Google Scholar
  23. 23.
    Guichardet, A.: Une caractérisation des algébres de von Neumann discrétes. Bull.Soc.Math.France 89, 77–101 (1961).Google Scholar
  24. 24.
    Ionescu-Tulcea, A. and Ionescu-Tulcea C.: On the lifting property (1). J. of Math.Anal. and Applic. 3, 537–546 (1961).CrossRefGoogle Scholar
  25. 25.
    Jacobson, N. and Rickart, C.: Homomorphisms of Jordan rings. Trans.Amer.Math.Soc. 69, 479–502 (1950).Google Scholar
  26. 26.
    Kadison, R.V.: Isometries of operator algebras, Ann.Math. 54, 325–338 (1951).Google Scholar
  27. 27.
    : A generalized Schwarz inequality and algebraic invariants for operator algebras, Ann.Math. 56, 494–503 (1952).Google Scholar
  28. 28.
    : Unitary invariants for representations of operator algebras, Ann.Math. 66, 304–379 (1957).Google Scholar
  29. 29.
    : The trace in finite operator algebras., Proc.Amer. Math.Soc. 12, 973–977 (1961).Google Scholar
  30. 30.
    :: Normalcy in operator algebras, Duke Math.J. 29, 459–464 (1962).CrossRefGoogle Scholar
  31. 31.
    : The trace in finite operator algebras, Lecture notes, Columbia University (1963).Google Scholar
  32. 32.
    : Transformations of states in operator theory and dynamics, Topology, suppl. 2, 177–198 (1965).Google Scholar
  33. 33.
    Kadison, R.V. and Ringrose, J.R.: Derivations and automorphisms of operator algebras, Commun.math.Phys. 4, 32–63 (1967).CrossRefGoogle Scholar
  34. 34.
    Kadison, R.V. and Singer, I.M.: Extensions of pure states, Amer. J.Math. 81, 383–400 (1959).Google Scholar
  35. 35.
    Kovács, I. and Szücs, J.: Ergodic type theorems in von Neumann algebras, Acta.Sc.Math. 27, 233–246 (1966).Google Scholar
  36. 36.
    Neumark, M.A.: On a representation of additive operator set functions, C.R. (Doklady) Acad.Sci. URSS 41, 359–361 (1943).Google Scholar
  37. 37.
    Phelps, R.R.: Extreme positive operators and homomorphisms, Trans.Amer.Soc. 108, 265–274 (1963).Google Scholar
  38. 38.
    Powers, R.T.: Algebras of unbounded operators, II, To appear.Google Scholar
  39. 39.
    Prosser, R.: On the ideal structure of operator algebras, Mem. Amer.Math.Soc. 45, 1–28 (1963).Google Scholar
  40. 40.
    Riesz, F. and Nagy, B.Sz.: Functional Analysis, Ungar, New York (1955).Google Scholar
  41. 41.
    Russo, B.: Linear mappings of operator algebras, Proc.Amer.Math.Soc. 17, 1019–1022 (1966).Google Scholar
  42. 42.
    Russo, B. and Dye, H.A.: A note on unitary operators in C*-algebras, Duke Math.J. 33, 413–416 (1966).CrossRefGoogle Scholar
  43. 43.
    Sakai, S.: On a characterization of type I C*-algebras, Bull. Amer.Math.Soc. 72, 508–511 (1966).Google Scholar
  44. 44.
    Schwartz, J.: Two finite, non hyperfinite, non isomorphic factors, Comm.Pure Appl.Math. 16, 19–26 (1963).Google Scholar
  45. 45.
    Semadeni, Z.: Free compact convex sets, Bull,Acad.Sc.Pol. 13, 141–146 (1965).Google Scholar
  46. 46.
    Stinespring, W.F.: Positive functions on Cu*-algebras, Proc.Amer. Math.Soc. 6, 211–216 (1955).Google Scholar
  47. 47.
    Størmer, E.: Positive linear maps of operator algebras, Acta math. 110, 233–278 (1963).Google Scholar
  48. 48.
    :: On the Jordan structure of Cu*-algebras, Trans. Amer. Math.Soc. 120, 438–447 (1965).Google Scholar
  49. 49.
    : On anti-automorphisms of von Neumann algebras, Pacific J.Math. 21, 349–370 (1967).Google Scholar
  50. 50.
    ": On extremal maps of operator algebras, Aarhus University (1966).Google Scholar
  51. 51.
    : On partially ordered vector spaces and their duals, with applications to simplexes and Cu*-algebras, Proc. London Math.Soc. 18, 245–265 (1968).Google Scholar
  52. 52.
    Størmer, E.: Large groups of automorphisms of C*-algebras, Commun.math.Phys. 5, 1–22 (1967).CrossRefGoogle Scholar
  53. 53.
    : Positive linear maps and Jordan homomorphisms, Oslo University (1969).Google Scholar
  54. 54.
    : States and invariant maps of operator algebras, J.Fnal.Anal. 5, 44–65 (1970).CrossRefGoogle Scholar
  55. 55.
    : On projection maps of von Neumann algebras, Math. Scand. 30, 46–50 (1972).Google Scholar
  56. 56.
    Takesaki, M.: Conditional expectations in von Neumann algebras, J.Fnal.Anal. 9, 306–321 (1972).CrossRefGoogle Scholar
  57. 57.
    Tomiyama, J.: On the projection of norm one in Wu*-algebras, Proc.Japan Acad. 33, 608–612 (1957).Google Scholar
  58. 58.
    58.: On the projection of norm one in W*-algebras, III, Tôhoku Math.J. 11, 125–129 (1959).Google Scholar
  59. 59.
    : The extension property of von Neumann algebras and a class of C*-algebras associated to them, To appear.Google Scholar
  60. 60.
    Wigner, E.P.: Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektren, Friedr. Vieweg, Braunschweig (1931).Google Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • Erling Størmer
    • 1
  1. 1.University of OsloOsloNorway

Personalised recommendations