Extensions of nonlinear completely positive maps

Fumio HIAI; Yoshihiro NAKAMURA

doi:10.2969/jmsj/03930367

Fumio HIAI, Yoshihiro NAKAMURA

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JOURNAL FREE ACCESS

1987 Volume 39 Issue 3 Pages 367-384

DOI https://doi.org/10.2969/jmsj/03930367

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Published: 1987 Received: October 21, 1985 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) T. Ando and M. D. Choi, Non-linear completely positive maps, Aspects of Positivity in Functional Analysis, R. Nagel et al. eds., North-Holland, Amsterdam, 1986, pp. 3-13.
2) W. B. Arveson, Subalgebras of C^*-algebras, Acta Math., 123 (1969), 141-224.
3) W. B. Arveson, Nonlinear states on C^*-algebras, Operator Algebras and Mathematical Physics, Contemporary Math., Vol. 62, Amer. Math. Soc., 1987, pp. 283-343.
4) M. D. Choi, A simple C^*-algebra generated by two finite-order unitaries, Canad. J. Math., 31 (1979), 867-880.
5) M. D. Choi and E. G. Effros, Injectivity and operator spaces, J. Funct. Anal., 24 (1977), 156-209.
6) M. D. Choi and E. G. Effros, Nuclear C^*-algebras and the approximation property, Amer. J. Math., 100 (1978), 61-79.
7) E. G. Effros and E. C. Lance, Tensor products of operator algebras, Adv. in Math., 25 (1977), 1-34.
8) C. S. Herz, Fonctions opérant sur les fonctions définies-positives, Ann. Inst. Fourier (Grenoble), 13 (1963), 161-180.
9) E. C. Lance, Tensor products of non-unital C^*-algebras, J. London Math. Soc., 12 (1976), 160-168.
10) E. C. Lance, Tensor products and nuclear C^*-algebras, Operator Algebras and Application, Proc. Symp. Pure Math., Vol. 38, Part 1, Amer. Math. Soc., 1982, pp. 379-399.
11) W. Rudin, Positive definite sequences and absolutely monotonic functions, Duke Math. J., 26 (1959), 617-622.
12) I. J. Schoenberg, Positive definite functions on spheres, Duke Math. J., 9 (1942), 96-108.
13) W. F. Stinespring, Positive functions on C^*-algebras, Proc. Amer. Math. Soc., 6 (1955), 211-216.
14) M. Takesaki, Theory of Operator Algebras I, Springer-Verlag, New York, 1979.

Right : [1] T. Ando and M. D. Choi, Non-linear completely positive maps, Aspects of Positivity in Functional Analysis, R. Nagel et al. eds., North-Holland, Amsterdam, 1986, pp. 3-13.
[2] W. B. Arveson, Subalgebras of C^*-algebras, Acta Math., 123 (1969), 141-224.
[3] W. B. Arveson, Nonlinear states on C^*-algebras, Operator Algebras and Mathematical Physics, Contemporary Math., Vol. 62, Amer. Math. Soc., 1987, pp. 283-343.
[4] M. D. Choi, A simple C^*-algebra generated by two finite-order unitaries, Canad. J. Math., 31 (1979), 867-880.
[5] M. D. Choi and E. G. Effros, Injectivity and operator spaces, J. Funct. Anal., 24 (1977), 156-209.
[6] M. D. Choi and E. G. Effros, Nuclear C^*-algebras and the approximation property, Amer. J. Math., 100 (1978), 61-79.
[7] E. G. Effros and E. C. Lance, Tensor products of operator algebras, Adv. in Math., 25 (1977), 1-34.
[8] C. S. Herz, Fonctions opérant sur les fonctions définies-positives, Ann. Inst. Fourier (Grenoble), 13 (1963), 161-180.
[9] E. C. Lance, Tensor products of non-unital C^*-algebras, J. London Math. Soc., 12 (1976), 160-168.
[10] E. C. Lance, Tensor products and nuclear C^*-algebras, Operator Algebras and Application, Proc. Symp. Pure Math., Vol. 38, Part 1, Amer. Math. Soc., 1982, pp. 379-399.
[11] W. Rudin, Positive definite sequences and absolutely monotonic functions, Duke Math. J., 26 (1959), 617-622.
[12] I. J. Schoenberg, Positive definite functions on spheres, Duke Math. J., 9 (1942), 96-108.
[13] W. F. Stinespring, Positive functions on C^*-algebras, Proc. Amer. Math. Soc., 6 (1955), 211-216.
[14] M. Takesaki, Theory of Operator Algebras I, Springer-Verlag, New York, 1979.

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