Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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THE GENERALIZED NORMAL STATE SPACE AND UNITAL NORMAL COMPLETELY POSITIVE MAP

  • Published : 1998.02.01
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Abstract

By introducing the notion of a generalized normal state space, we give a necessary and sufficient condition for that there exists a unital normal completely map from a von Neumann algebra into another, in terms of their generalized normal state spaces.

Keywords

References

  1. Compact Convex Sets and Boundary integral L.M. Alfsen
  2. Acta Math. v.123 Subalgebras of $C^*$-algebras W.B. Arveson
  3. Illnois J. Math. v.18 A Schwarz inequality for positive linear maps on $C^*$-algebras M.D. Choi
  4. $C^*$-algebras J. Dixmier
  5. Contemporary Math. v.167 Some quantizations and reflections inspired by the Gelfand Naimark theorem E.G. Effros
  6. J. Funct. Anal. (to appear) Matrix convexity: operator analogues of the bipolar and Hahn-Banach theorems E.G. Efferos;S. Winkler
  7. Canad. J. Math. v.44 $C^*$-convexity and matricial ranges D. R. Farenick
  8. Trans. Amer. Math. Soc. (to appear) $C^*$-extreme points in the generalised state spaces of a $C^*$-algebras D.R. Farenick;P.B. Morenz
  9. Trans. Amer. Math. Soc. (to appear) $C^*$-extreme points in the generalised state spaces of a $C^*$-algebras D.R. Farenick;P.B. Morenz
  10. Proc. Amer. Math. Soc. (to appear) The structure of $C^*$-extreme points in spaces of completely positive linar maps on $C^*$-algebras D.R. Farenick;H. Zhou
  11. J. Operator Theopy v.32 Decomposition of completely positive maps I. Fujimoto
  12. A Hilbert Space Problem Book P.R. Halmos
  13. Trans. Amer. Math. Soc. v.266 $C^*$-extreme points A. Hopenwasser;R.L. Moore;V.I. Paulsen
  14. Fundamentals of the Theory of Operator Algebras v.Ⅰ R.V. Kadison;J.R. Ringrose
  15. Notes on the Gelfand-Naimark theorem Contemporary Mathematics v.167 R.V. Kadison
  16. AMS Special Session Commemorating the First Fifty Years of $C^*$-algebras Theory $C^*$-algebras: 1943-1993;A Fifty Year Celebration
  17. Amer. Math. Soc. R.S. Doran(ed.)
  18. Proc. Amer. Math. Soc. v.106 Multi-states on $C^*$-algebras A. Kaplan
  19. RIM-GARC Preprint series 95-31 The *-isomorphism between unital $C^*$-algebras described by genertizes state spaces S.G. Lee
  20. RIM-GARC Preprint series 96-19 The $M^∞$-biomodules of unital $C^*$-algebras S.G. Lee
  21. RIM-GARC Preprint series 97-3 Conditional expection from the free product of $C^*$-algebras onto one of its factor algebras S.G. Lee
  22. Canad. J. Math. v.46 The structure of $C^*$-convex sets P.B. Morenz
  23. Completely Bounded Maps and Dilations V.I. Paulsen
  24. $C^*$-algebras and Their Automorphism Groups G.K. Pedersen
  25. Ordered Topological VEctor Spaces A.L. Peressini
  26. Functional Analysis(second edition) W. Rudin
  27. Amer. J. Math. v.102 Matrix ranges for Hilbert space operators R.R. Smith;J.D. Ward
  28. J. Functional Anal. v.40 The geometric structure of generalizedstate spaces R.R. Smith;J.D. Ward
  29. Modular Theory of Operator Algebras S. Stratila
  30. Lectures on von Neumann algebras(English Version) S. Stratila;L. Zsido
  31. Theory of Operator Algebras Ⅰ M. Takesaki
  32. Proc. Edin. Math. Soc. v.36 Extreme n-positive linear maps S.K. Tsui
  33. On matrix order and convexity Functional Analysis: Surveys and Resent Results v.90 G. Wittstock