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Volumn 303, Issue 2, 2011, Pages 555-594

Factorization and Dilation Problems for Completely Positive Maps on von Neumann Algebras

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EID: 79953095838     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-011-1216-y     Document Type: Article
Times cited : (107)

References (36)
  • 1
    • 0001216606 scopus 로고
    • Conditional expectations in von Neumann algebras and a theorem of Takesaki
    • Accardi L., Cecchini C.: Conditional expectations in von Neumann algebras and a theorem of Takesaki. J. Funct. Analysis 45, 245-273 (1982).
    • (1982) J. Funct. Analysis , vol.45 , pp. 245-273
    • Accardi, L.1    Cecchini, C.2
  • 2
    • 33646744372 scopus 로고    scopus 로고
    • On ergodic theorems for free group actions on noncommutative spaces
    • Anantharaman-Delaroche C.: On ergodic theorems for free group actions on noncommutative spaces. Probab. Theory Rel. Fields 135, 520-546 (2006).
    • (2006) Probab. Theory Rel. Fields , vol.135 , pp. 520-546
    • Anantharaman-Delaroche, C.1
  • 5
    • 0001336132 scopus 로고
    • Three observations on linear algebra
    • Birkhoff G.: Three observations on linear algebra. Univ. Nac. Tucuan, Revista A 5, 147-151 (1946).
    • (1946) Univ. Nac. Tucuan, Revista A , vol.5 , pp. 147-151
    • Birkhoff, G.1
  • 7
    • 0016522050 scopus 로고
    • Completely positive linear maps on complex matrices
    • Choi M.-D.: Completely positive linear maps on complex matrices. Lin. Alg. Applic. 10, 285-290 (1975).
    • (1975) Lin. Alg. Applic. , vol.10 , pp. 285-290
    • Choi, M.-D.1
  • 8
    • 0008725475 scopus 로고
    • A note on extreme positive definite matrices
    • Christensen J. P. R., Vesterstrøm J.: A note on extreme positive definite matrices. Math. Ann 244, 65-68 (1979).
    • (1979) Math. Ann , vol.244 , pp. 65-68
    • Christensen, J.P.R.1    Vesterstrøm, J.2
  • 11
    • 84963069488 scopus 로고
    • Residual properties of infinite soluble groups
    • Gruenberg K. W.: Residual properties of infinite soluble groups. Proc. London Math. Soc. 3(7), 29-62 (1957).
    • (1957) Proc. London Math. Soc. , vol.3 , Issue.7 , pp. 29-62
    • Gruenberg, K.W.1
  • 12
    • 84974003474 scopus 로고
    • λ, 0 & λ & 1
    • λ, 0 & λ & 1. Pacific J. Math. 137(2), 265-310 (1989).
    • (1989) Pacific J. Math. , vol.137 , Issue.2 , pp. 265-310
    • Haagerup, U.1
  • 13
    • 0013126091 scopus 로고
    • Grothendieck type norms for bilinear forms on C*-algebras
    • Haagerup U., Itoh T.: Grothendieck type norms for bilinear forms on C*-algebras. J. Operator Theory 34, 263-283 (1995).
    • (1995) J. Operator Theory , vol.34 , pp. 263-283
    • Haagerup, U.1    Itoh, T.2
  • 14
    • 50249087425 scopus 로고    scopus 로고
    • The Effros-Ruan conjecture for bilinear maps on C*-algebras
    • Haagerup U., Musat M.: The Effros-Ruan conjecture for bilinear maps on C*-algebras. Invent. Math. 174(1), 139-163 (2008).
    • (2008) Invent. Math. , vol.174 , Issue.1 , pp. 139-163
    • Haagerup, U.1    Musat, M.2
  • 15
    • 77954646143 scopus 로고    scopus 로고
    • Noncommutative Riesz transforms-a probabilistic approach
    • Junge M., Mei T.: Noncommutative Riesz transforms-a probabilistic approach. Amer. J. Math. 132(3), 611-680 (2010).
    • (2010) Amer. J. Math. , vol.132 , Issue.3 , pp. 611-680
    • Junge, M.1    Mei, T.2
  • 19
    • 0000294483 scopus 로고
    • On nonsemisplit extensions, tensor products and exactness of group C*-algebras
    • Kirchberg E.: On nonsemisplit extensions, tensor products and exactness of group C*-algebras. Invent. Math. 112(3), 449-489 (1993).
    • (1993) Invent. Math. , vol.112 , Issue.3 , pp. 449-489
    • Kirchberg, E.1
  • 22
    • 0000434290 scopus 로고
    • Markov dilations on W*-algebras
    • Kümmerer B.: Markov dilations on W*-algebras. J. Funct. Analysis 63, 139-177 (1985).
    • (1985) J. Funct. Analysis , vol.63 , pp. 139-177
    • Kümmerer, B.1
  • 25
    • 1542365806 scopus 로고
    • On Birkhoff's theorem for doubly stochastic completely positive maps on matrix algebras
    • Landau L. J., Streater R. F.: On Birkhoff's theorem for doubly stochastic completely positive maps on matrix algebras. Lin. Alg. Applic. 193, 107-127 (1993).
    • (1993) Lin. Alg. Applic. , vol.193 , pp. 107-127
    • Landau, L.J.1    Streater, R.F.2
  • 26
    • 55549146077 scopus 로고    scopus 로고
    • Tent spaces associated with semigroups of operators
    • Mei T.: Tent spaces associated with semigroups of operators. J. Funct. Anal 255, 3356-3406 (2008).
    • (2008) J. Funct. Anal , vol.255 , pp. 3356-3406
    • Mei, T.1
  • 27
    • 67650649520 scopus 로고    scopus 로고
    • Unital quantum channels - convex structure and revivals of Birkhoff's theorem
    • Mendl C. B., Wolf M. M.: Unital quantum channels - convex structure and revivals of Birkhoff's theorem. Commun. Math. Phys. 289, 1057-1096 (2009).
    • (2009) Commun. Math. Phys. , vol.289 , pp. 1057-1096
    • Mendl, C.B.1    Wolf, M.M.2
  • 28
    • 7244231166 scopus 로고    scopus 로고
    • About the QWEP conjecture
    • Ozawa N.: About the QWEP conjecture. Internat. J. Math. 15, 501-530 (2004).
    • (2004) Internat. J. Math. , vol.15 , pp. 501-530
    • Ozawa, N.1
  • 29
    • 0030195280 scopus 로고    scopus 로고
    • The Operator Hilbert SpaceOH, sComplex Interpolation and Tensor Norms
    • Amer. math. Soc., Providence, RI
    • Pisier, G.: The Operator Hilbert SpaceOH, sComplex Interpolation and Tensor Norms. Mem. Amer. Math. Soc. Number 585, Vol. 122, Providence, RI: Amer. math. Soc., 1996.
    • (1996) Mem. Amer. Math. Soc. , vol.122 , Issue.585
    • Pisier, G.1
  • 30
    • 0036026040 scopus 로고    scopus 로고
    • Grothendieck's theorem for operator spaces
    • Pisier G., Shlyakhtenko D.: Grothendieck's theorem for operator spaces. Invent. Math. 150, 185-217 (2002).
    • (2002) Invent. Math. , vol.150 , pp. 185-217
    • Pisier, G.1    Shlyakhtenko, D.2
  • 31
    • 77950602933 scopus 로고    scopus 로고
    • A Markov dilation for self-adjoint Schur multipliers
    • Ricard E.: A Markov dilation for self-adjoint Schur multipliers. Proc. Amer. Math. Soc. 136(12), 4365-4372 (2008).
    • (2008) Proc. Amer. Math. Soc. , vol.136 , Issue.12 , pp. 4365-4372
    • Ricard, E.1
  • 32
    • 84966254756 scopus 로고
    • An Alternierende Verfahren for general positive operators
    • Commun. Math. Phys
    • Rota, G.-C.: An Alternierende Verfahren for general positive operators. Bull. Amer. Math. Soc. 68 (1962), 95-102; Commun. Math. Phys. 106(1), 91-103, 1986.
    • (1962) Bull. Amer. Math. Soc. , vol.68-106 , Issue.1
    • Rota, G.-C.1
  • 33
    • 28844438788 scopus 로고    scopus 로고
    • Entanglement of assistance and multipartite state distillation
    • Smolin J. A., Verstraete F., Winter A.: Entanglement of assistance and multipartite state distillation. Phys. Rev. A 72, 052317 (2005).
    • (2005) Phys. Rev. A , vol.72 , pp. 052317
    • Smolin, J.A.1    Verstraete, F.2    Winter, A.3
  • 34
    • 33646924067 scopus 로고
    • Conditional expectations in von Neumann algebras
    • Takesaki M.: Conditional expectations in von Neumann algebras. J. Funct. Anal. 9, 306-321 (1972).
    • (1972) J. Funct. Anal. , vol.9 , pp. 306-321
    • Takesaki, M.1
  • 36
    • 79953108262 scopus 로고    scopus 로고
    • also available at http://arxiv. org/abs/quant-ph/0504166v1
    • Werner's R.: open problems in quantum information theory web site http://www. imaph. tu-bs. de/qi/problems/problems. html., also available at http://arxiv. org/abs/quant-ph/0504166v1, 2005.
    • (2005) Open problems in quantum information theory web site
    • Werner's, R.1


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