메뉴 건너뛰기




Volumn 24, Issue 2, 2006, Pages 103-125

On k-decomposability of positive maps

Author keywords

k (co)positive maps; k decomposable; St rmer condition; Tomita Takesaki

Indexed keywords


EID: 33646418717     PISSN: 07230869     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.exmath.2005.07.002     Document Type: Article
Times cited : (16)

References (31)
  • 2
    • 84972558603 scopus 로고
    • Some properties of modular conjugation operator of a von Neumann algebra and a non-commutative Radon-Nikodym theorem with a chain rule, Pacific
    • H. Araki, Some properties of modular conjugation operator of a von Neumann algebra and a non-commutative Radon-Nikodym theorem with a chain rule, Pacific J. Math. 50 (1974) 309-354.
    • (1974) J. Math. , vol.50 , pp. 309-354
    • Araki, H.1
  • 3
    • 84995999330 scopus 로고
    • Relative Hamiltonian for faithful normal states of a van Neumann algebra
    • H. Araki, Relative Hamiltonian for faithful normal states of a van Neumann algebra, Publ. Res. Inst. Math. Sci. Kyoto 9 (1973) 165-209.
    • (1973) Publ. Res. Inst. Math. Sci. Kyoto , vol.9 , pp. 165-209
    • Araki, H.1
  • 4
    • 34250491179 scopus 로고
    • Subalgebras of C*-algebras
    • W. Arveson, Subalgebras of C*-algebras, Acta Math. 123 (1969) 141-224.
    • (1969) Acta Math. , vol.123 , pp. 141-224
    • Arveson, W.1
  • 6
    • 0016522050 scopus 로고
    • Completely positive maps on complex matrices
    • M.-D. Choi, Completely positive maps on complex matrices, Linear Algebra Appl. 10 (1975) 285-290.
    • (1975) Linear Algebra Appl. , vol.10 , pp. 285-290
    • Choi, M.-D.1
  • 7
    • 0003143974 scopus 로고
    • Positive semidefinite biquadratic forms
    • M.-D. Choi, Positive semidefinite biquadratic forms, Linear Algebra Appl. 12 (1975) 95-100.
    • (1975) Linear Algebra Appl. , vol.12 , pp. 95-100
    • Choi, M.-D.1
  • 8
    • 0011048773 scopus 로고
    • Caractérisation des espaces vectoriels ordonnés sous-jacents aux algèbres de von Neumann
    • A. Connes, Caractérisation des espaces vectoriels ordonnés sous-jacents aux algèbres de von Neumann, Ann. Inst. Fourier Grenoble 24 (1974) 121-155.
    • (1974) Ann. Inst. Fourier Grenoble , vol.24 , pp. 121-155
    • Connes, A.1
  • 9
    • 25444505461 scopus 로고
    • Les C*-Algèbres et leurs Représentations
    • Paris
    • J. Dixmier, Les C*-Algèbres et leurs Représentations, Gauthier-Villars, Paris, 1964.
    • (1964) Gauthier-Villars
    • Dixmier, J.1
  • 10
    • 0038482959 scopus 로고    scopus 로고
    • Duality for positive linear maps in matrix algebras
    • M.-H. Eom, S.-H. Kye, Duality for positive linear maps in matrix algebras, Math. Scand. 86 (2000) 130-142.
    • (2000) Math. Scand. , vol.86 , pp. 130-142
    • Eom, M.-H.1    Kye, S.-H.2
  • 11
    • 25444489307 scopus 로고    scopus 로고
    • Atomic positive linear maps in matrix algebras
    • K.-C. Ha, Atomic positive linear maps in matrix algebras, Publ. RIMS Kyoto Univ. 34 (1998) 591-599.
    • (1998) Publ. RIMS Kyoto Univ. , vol.34 , pp. 591-599
    • Ha, K.-C.1
  • 12
    • 0042376719 scopus 로고    scopus 로고
    • Separability of mixed states: Necessary and sufficient conditions
    • M. Horodecki, P. Horodecki, R. Horodecki, Separability of mixed states: necessary and sufficient conditions, Phys. Lett. A 223 (1996) 1-8.
    • (1996) Phys. Lett. A , vol.223 , pp. 1-8
    • Horodecki, M.1    Horodecki, P.2    Horodecki, R.3
  • 13
    • 33144470750 scopus 로고
    • Transformations of states in operator theory and dynamics
    • R.V. Kadison, Transformations of states in operator theory and dynamics, Topology 3 (1965) 177-198.
    • (1965) Topology , vol.3 , pp. 177-198
    • Kadison, R.V.1
  • 14
    • 0011277919 scopus 로고
    • Indecomposable extreme positive linear maps in matrix algebras
    • H.-J. Kim, S.-H. Kye, Indecomposable extreme positive linear maps in matrix algebras, Bull. London Math. Soc. 26 (1994) 575-581.
    • (1994) Bull. London Math. Soc. , vol.26 , pp. 575-581
    • Kim, H.-J.1    Kye, S.-H.2
  • 15
    • 4043107730 scopus 로고    scopus 로고
    • A family of positive linear maps in matrix algebras
    • A. Kossakowski, A family of positive linear maps in matrix algebras, Open Systems Inform. Dynamics 10 (2003) 213-220.
    • (2003) Open Systems Inform. Dynamics , vol.10 , pp. 213-220
    • Kossakowski, A.1
  • 16
    • 4043086683 scopus 로고
    • Transformations between quantum states
    • W.A. Majewski, Transformations between quantum states, Rep. Math. Phys. 8 (1975) 295-307.
    • (1975) Rep. Math. Phys. , vol.8 , pp. 295-307
    • Majewski, W.A.1
  • 17
    • 84990634536 scopus 로고
    • Dynamical semigroups in the algebraic formulation of statistical mechanics
    • W.A. Majewski, Dynamical semigroups in the algebraic formulation of statistical mechanics, Fortschr. Phys. 32 (1) (1984) 89-133.
    • (1984) Fortschr. Phys. , vol.32 , Issue.1 , pp. 89-133
    • Majewski, W.A.1
  • 18
    • 0008234537 scopus 로고    scopus 로고
    • Separable and entangled states of composite quantum systems; rigorous description
    • W.A. Majewski, Separable and entangled states of composite quantum systems; rigorous description, Open Systems Inform. Dynamics 6 (1999) 79-88.
    • (1999) Open Systems Inform. Dynamics , vol.6 , pp. 79-88
    • Majewski, W.A.1
  • 19
    • 33646395807 scopus 로고    scopus 로고
    • Quantum Stochastic Dynamical Semigroup Dynamics of Dissipations
    • P. Garbaczewski, R. Olkiewicz (Eds.) Springer, Berlin
    • W.A. Majewski, Quantum Stochastic Dynamical Semigroup, in: Dynamics of Dissipations, P. Garbaczewski, R. Olkiewicz (Eds.), Lecture Notes in Physics, vol. 597, Springer, Berlin, 2002, pp. 305-316.
    • (2002) Lecture Notes in Physics , vol.597 , pp. 305-316
    • Majewski, W.A.1
  • 21
    • 0032475781 scopus 로고    scopus 로고
    • Detailed balance and quantum dynamical maps
    • W.A. Majewski, R. Streater, Detailed balance and quantum dynamical maps, J. Phys. A: Math. Gen. 31 (1998) 7981-7995.
    • (1998) J. Phys. A: Math. Gen. , vol.31 , pp. 7981-7995
    • Majewski, W.A.1    Streater, R.2
  • 22
    • 0037574296 scopus 로고    scopus 로고
    • Separability criterion for density matrices
    • A. Peres, Separability criterion for density matrices, Phys. Rev. Lett. 77 (1996) 1413.
    • (1996) Phys. Rev. Lett. , vol.77 , pp. 1413
    • Peres, A.1
  • 23
    • 84976128764 scopus 로고
    • Schwarz inequalities and the decomposition of positive maps on *-algebras
    • G. Robertson, Schwarz inequalities and the decomposition of positive maps on *-algebras, Math. Proc. Cambridge Philos. Soc. 94 (1983) 291-296.
    • (1983) Math. Proc. Cambridge Philos. Soc. , vol.94 , pp. 291-296
    • Robertson, G.1
  • 24
    • 0000896652 scopus 로고
    • Positive linear maps of operator algebras
    • E. Størmer, Positive linear maps of operator algebras, Acta Math. 110 (1963) 233-278.
    • (1963) Acta Math. , vol.110 , pp. 233-278
    • Størmer, E.1
  • 25
    • 84859473104 scopus 로고
    • On the Jordan structure of C*-algebras
    • E. Størmer, On the Jordan structure of C*-algebras, Trans. Amer. Math. Soc. 120 (1965) 438-447.
    • (1965) Trans. Amer. Math. Soc. , vol.120 , pp. 438-447
    • Størmer, E.1
  • 26
    • 4043151062 scopus 로고
    • Decomposition of positive projections on C*-algebras
    • E. Størmer, Decomposition of positive projections on C*-algebras, Math. Ann. 247 (1980) 21-41.
    • (1980) Math. Ann. , vol.247 , pp. 21-41
    • Størmer, E.1
  • 27
    • 84966261616 scopus 로고
    • Decomposable positive maps on C* -algebras
    • E. Størmer, Decomposable positive maps on C* -algebras, Proc. Amer. Math. Soc. 86 (1982) 402-404.
    • (1982) Proc. Amer. Math. Soc. , vol.86 , pp. 402-404
    • Størmer, E.1
  • 28
    • 0040781865 scopus 로고
    • Extension of positive maps into ℬ(H)
    • E. Størmer, Extension of positive maps into ℬ(H), J. Funct. Anal. 66 (1986) 235-254.
    • (1986) J. Funct. Anal. , vol.66 , pp. 235-254
    • Størmer, E.1
  • 29
    • 0040275491 scopus 로고
    • On the difference of n-positivity and complete positivity in C*-algebras
    • J. Tomiyama, On the difference of n-positivity and complete positivity in C*-algebras, J. Funct. Anal. 49 (1982) 1-9.
    • (1982) J. Funct. Anal. , vol.49 , pp. 1-9
    • Tomiyama, J.1
  • 31
    • 0000260392 scopus 로고
    • Positive maps of low dimensional matrix algebras
    • S.L. Woronowicz, Positive maps of low dimensional matrix algebras, Rep. Math. Phys. 10 (1976) 165-183.
    • (1976) Rep. Math. Phys. , vol.10 , pp. 165-183
    • Woronowicz, S.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.