Symmetrically Completely Bounded Linear Maps Between C*-Algebras
Canadian mathematical bulletin, Tome 35 (1992) no. 2, pp. 278-286

Voir la notice de l'article provenant de la source Cambridge University Press

We study the properties of a new class SCB(L, B) of bounded linear maps, called symmetrically completely bounded maps, from a linear subspace L of a C* -algebra to another C*-algebra B. This class contains the class of all completely bounded linear maps from L to B. In particular, we obtain a representation theorem for maps in SCB(L, B) when B is the algebra of all bounded linear operators on a Hilbert space.
DOI : 10.4153/CMB-1992-039-6
Mots-clés : 46L05, 47D15
Tang, Wai-Shing. Symmetrically Completely Bounded Linear Maps Between C*-Algebras. Canadian mathematical bulletin, Tome 35 (1992) no. 2, pp. 278-286. doi: 10.4153/CMB-1992-039-6
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[1] 1. Arveson, W. B., Subalgebras of C*-algebras, Acta Math. 123(1969), 141–224. Google Scholar

[2] 2. Choi, M.-D. and Effros, E. G., Injectivity and operator spaces, J. Func. Anal. 24(1977), 156–209. Google Scholar

[3] 3. Christensen, E. and Sinclair, A. M., Representations of completely bounded multilinear operators, J. Func. Anal. 72(1987), 151–181. Google Scholar

[4] 4. Haagerup, U., Solution of the similarity problem for cyclic representations of C* -algebras, Ann. Math. 118(1983), 215–240. Google Scholar

[5] 5. Huruya, T. and Tomiyama, J., Completely bounded maps of C-algebras, J. Operator Theory 10(1983), 141–152. Google Scholar

[6] 6. Paulsen, V. I., Every completely polynomially bounded operator is similar to a contraction, J. Func. Anal. 55(1984), 1–17. Google Scholar

[7] 7. Paulsen, V. I., Completely bounded maps and dilations, Pitman Research Notes in Mathematics Series, 146 (1986), Longman Scientific & Technical, U.K. Google Scholar

[8] 8. Smith, R. R., Completely bounded maps between C* -algebras, J. London Math. Soc. (2). 27(1983), 157– 166. Google Scholar

[9] 9. Stinespring, W. F., Positive functions on C*-algebras, Proc. Amer. Math Soc. 6(1955), 211–216. Google Scholar

[10] 10. Stormer, E., On the Jordan structure of C*-algebras, Trans. Amer. Math Soc. 120(1965), 438–447. Google Scholar

[11] 11. Stormer, E., Decomposition of positive projections on C*-algebras, Math. Ann. 27(1980), 21–11. Google Scholar

[12] 12. Stormer, E., Decomposable positive maps on C*-algebras, Proc. Amer. Math. Soc, 86(1982), 402–104. Google Scholar

[13] 13. Tomiyama, J., On the transpose map of matrix algebras, Proc. Amer. Math. Soc. 88(1983), 635–638. Google Scholar

[14] 14. Wittstock, G., Extension of completely bounded C* -module homomorphisms, in “Proc. Conference on Operator Algebras and Group Representations”, Neptune (1980), Pitman, New York, (1984). Google Scholar

[15] 15. Woronowicz, S. L., Positive maps of low dimensional matrix algebras,Rep. Math. Phys. 10(1976), 165–183. Google Scholar

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