A decomposition theorem in a Banach *-algebra related to completely bounded maps on C*-algebras

Takashi ITOH

doi:10.2969/jmsj/04330619

A decomposition theorem in a Banach *-algebra related to completely bounded maps on C^*-algebras

Takashi ITOH

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JOURNAL FREE ACCESS

1991 Volume 43 Issue 3 Pages 619-630

DOI https://doi.org/10.2969/jmsj/04330619

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Published: 1991 Received: February 23, 1990 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) C. J. K. Batty and D. W. Robinson, Positive one parameter semigroups on ordered Banach space, Acta Applicandae Mathematicae, 2 (1984), 221-296, D. Reidel Publishing Company.
2) D. P. Blecher and V. I. Paulsen, Tensor products of operator spaces, preprint.
3) E. Christensen, E. G. Effros and A. M. Sinclair, Completely bounded maps and C^*-algebraic cohomology, Inventiones Math., 90 (1987), 279-296.
4) E. B. Davies, The structure and ideal theory of the predual of a Banach lattice, Trans. Amer. Math. Soc., 131 (1968), 544-555.
5) E. G. Effros and R. Exel, On multilinear double commutant theorems, London Math. Soc., Lecture Note Seris, 135(1988), 81-94, Cambridge Univ. Press.
6) E. G. Effros and A. Kishimoto, Module maps and Hochschild-Johnson Cohomology, Indiana Univ. Math. J., 36(1987), 257-276.
7) U. Haagerup, Decomposition of completely bounded maps on operator algebras, unpublished manuscript 1980.
8) T. Huruya and J. Tomiyama, Completely bounded maps of C^*-algebras, J. Operator theory, 10(1983), 141-152.
9) T. Itoh, Completely bounded maps and a certain cross norm, Math. Japonica, 32 (1987), 239-249.
10) R. I. Loebl, A Hahn decomposition for linear maps, Pacific J. Math., 65 (1976), 119-133.
11) V. I. Paulsen, Completely bounded maps on C^*-algebras and invariant operator ranges, Proc. Amer. Math. Soc., 86(1982), 91-96.
12) V. I. Paulsen and R. R. Smith, Multilinear maps and tensor norms on operator systems, J. Funct. Anal., 73 (1987), 258-276.
13) Z-J. Ruan, In jectivity of operator space, Trans. Amer. Math. Soc. (to appear).
14) E. Stormer, Extension of positive maps into B(H), J. Funct. Anal., 66(1986), 235-254.
15) M. Takesaki, Theory of operator algebras 1, Springer, 1979.
16) S-K. J. Tsui, Decompositions of linear maps, Trans. Amer. Math. Soc., 230 (1977), 87-112.
17) G. Wittstock, Ein operatorwertiger Hahn-Banach Satz, J. Funct. Anal., 40(1981), 127-150.

Right : [1] C. J. K. Batty and D. W. Robinson, Positive one parameter semigroups on ordered Banach space, Acta Applicandae Mathematicae, 2 (1984), 221-296, D. Reidel Publishing Company.
[2] D. P. Blecher and V. I. Paulsen, Tensor products of operator spaces, preprint.
[3] E. Christensen, E. G. Effros and A. M. Sinclair, Completely bounded maps and C^*-algebraic cohomology, Inventiones Math., 90 (1987), 279-296.
[4] E. B. Davies, The structure and ideal theory of the predual of a Banach lattice, Trans. Amer. Math. Soc., 131 (1968), 544-555.
[5] E. G. Effros and R. Exel, On multilinear double commutant theorems, London Math. Soc., Lecture Note Seris, 135 (1988), 81-94, Cambridge Univ. Press.
[6] E. G. Effros and A. Kishimoto, Module maps and Hochschild-Johnson Cohomology, Indiana Univ. Math. J., 36 (1987), 257-276.
[7] U. Haagerup, Decomposition of completely bounded maps on operator algebras, unpublished manuscript 1980.
[8] T. Huruya and J. Tomiyama, Completely bounded maps of C^*-algebras, J. Operator theory, 10 (1983), 141-152.
[9] T. Itoh, Completely bounded maps and a certain cross norm, Math. Japonica, 32 (1987), 239-249.
[10] R. I. Loebl, A Hahn decomposition for linear maps, Pacific J. Math., 65 (1976), 119-133.
[11] V. I. Paulsen, Completely bounded maps on C^*-algebras and invariant operator ranges, Proc. Amer. Math. Soc., 86 (1982), 91-96.
[12] V. I. Paulsen and R. R. Smith, Multilinear maps and tensor norms on operator systems, J. Funct. Anal., 73 (1987), 258-276.
[13] Z-J. Ruan, In jectivity of operator space, Trans. Amer. Math. Soc. (to appear).
[14] E. Størmer, Extension of positive maps into B(H), J. Funct. Anal., 66(1986), 235-254.
[15] M. Takesaki, Theory of operator algebras 1, Springer, 1979.
[16] S-K. J. Tsui, Decompositions of linear maps, Trans. Amer. Math. Soc., 230 (1977), 87-112.
[17] G. Wittstock, Ein operatorwertiger Hahn-Banach Satz, J. Funct. Anal., 40 (1981), 127-150.

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