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

著者情報

ジャーナルフリー

1991 年 43 巻 3 号 p. 619-630

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

詳細

Published: 1991 Received: 1990/02/23 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: 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7) U. Haagerup, Decomposition of completely bounded maps on operator algebras, unpublished manuscript 1980.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.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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