An $n\times n$ matrix of linear maps of a $C^ *$-algebra
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- Proc. Amer. Math. Soc. 112 (1991), 709-712 Request permission
Abstract:
Every positive $n \times n$ matrix of linear functionals on a ${C^ * }$-algebra is completely positive. [3, Theorem 2.1] can be extended to the case of a bounded $n \times n$ matrix of linear functionals.References
- William B. Arveson, Subalgebras of $C^{\ast }$-algebras, Acta Math. 123 (1969), 141โ224. MR 253059, DOI 10.1007/BF02392388
- Uffe Haagerup, Injectivity and decomposition of completely bounded maps, Operator algebras and their connections with topology and ergodic theory (Buลteni, 1983) Lecture Notes in Math., vol. 1132, Springer, Berlin, 1985, pp.ย 170โ222. MR 799569, DOI 10.1007/BFb0074885
- Alexander Kaplan, Multi-states on $C^*$-algebras, Proc. Amer. Math. Soc. 106 (1989), no.ย 2, 437โ446. MR 972233, DOI 10.1090/S0002-9939-1989-0972233-2
- Vern I. Paulsen, Completely bounded maps and dilations, Pitman Research Notes in Mathematics Series, vol. 146, Longman Scientific & Technical, Harlow; John Wiley & Sons, Inc., New York, 1986. MR 868472
- Vern I. Paulsen and Ching Yun Suen, Commutant representations of completely bounded maps, J. Operator Theory 13 (1985), no.ย 1, 87โ101. MR 768304
- R. R. Smith, Completely bounded maps between $C^{\ast }$-algebras, J. London Math. Soc. (2) 27 (1983), no.ย 1, 157โ166. MR 686514, DOI 10.1112/jlms/s2-27.1.157
- R. R. Smith and J. D. Ward, Matrix ranges for Hilbert space operators, Amer. J. Math. 102 (1980), no.ย 6, 1031โ1081. MR 595006, DOI 10.2307/2374180
- W. Forrest Stinespring, Positive functions on $C^*$-algebras, Proc. Amer. Math. Soc. 6 (1955), 211โ216. MR 69403, DOI 10.1090/S0002-9939-1955-0069403-4
- Ching Yun Suen, Completely bounded maps on $C^\ast$-algebras, Proc. Amer. Math. Soc. 93 (1985), no.ย 1, 81โ87. MR 766532, DOI 10.1090/S0002-9939-1985-0766532-3 M. Takasaki, Theory of operator algebra 1, Springer-Verlag, Berlin, 1979.
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 112 (1991), 709-712
- MSC: Primary 46L05
- DOI: https://doi.org/10.1090/S0002-9939-1991-1069296-4
- MathSciNet review: 1069296