Factorization through matrix spaces for finite rank operators between c*-algebras

Duke Mathematical Journal

Volumn 100, Issue 2, 1999, Pages 299-319

  Junge, Marius ^a   Le Merdy, Christian ^b  

^a UNIVERSITY OF KIEL   (Germany)

^b UNIVERSITÉ DE FRANCHE COMTÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033570882     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-99-10011-1     Document Type: Article

References (33)

1. D. Blecher, The standard dual of an operator space, Pacific J. Math. 153 (1992), 15-30.
2. D. Blecher and V. Paulsen, Tensor products of operator spaces, J. Funct. Anal. 99 (1991), 262-292.
3. M. D. Choi and E. Effros, Nuclear C* -algebras and injectivity: The general case, Indiana Univ. Math. J. 26 (1977), 443-446.
4. M. D. Choi and E. Effros, Nuclear C* -algebras and the approximation property, Amer. J. Math. 100 (1978), 61-79.
5. E. Effros and U. Haagerup, Lifting problems and local reflexivity for C * -algebras, Duke Math. J. 52 (1985), 103-128.
6. 1 -spaces, to appear in Ann. of Math. (2).
7. E. Effros and Z.-J. Ruan, On approximation properties for operator spaces, Internat. J. Math. 1 (1990), 163-187.
8. E. Effros and Z.-J. Ruan, A new approach to operator spaces, Canad. Math. Bull. 34 (1991), 329-337.
9. E. Effros and Z.-J. Ruan, The Grothendieck-Pietsch and Dvoretzky-Rogers theorems for operator spaces, J. Funct. Anal. 122 (1994), 428-450.
10. E. Effros and Z.-J. Ruan, Mapping spaces and liftings for operator spaces, Proc. London Math. Soc. (3) 69 (1994), 171-197.
11. U. Haagerup, “Injectivity and decomposition of completely bounded maps” in Operator Algebras and Their Connections with Topology and Ergodic Theory (Busteni, 1983), Lecture Notes in Math. 1132, Springer-Verlag, Berlin, 1985, 170-222.
12. U. Haagerup and G. Pisier, Factorization of analytic functions with values in noncommutative Li -spaces and applications, Canad. J. Math. 41 (1989), 882-906.
13. U. Haagerup and G. Pisier, Bounded linear operators between C* -algebras, Duke Math. J. 71 (1993), 889-925.
14. M. Junge, Factorization theory for spaces of operators, Habilitationsschrift, Universitat Kiel, 1996.
15. M. Junge and G. Pisier, Bilinear forms on exact operator spaces and B(H) ® B(H), Geom. Funct. Anal. 5 (1995), 329-363.
16. E. Kirchberg, C * -nuclearity implies CPAP, Math. Nachr. 76 (1977), 203-212.
17. E. Kirchberg, Commutants of unitaries in UHF algebras and functorial properties of exactness, J. Reine Angew. Math. 452 (1994), 39-77.
18. C. Lance, On nuclear C* -algebras, J. Funct. Anal. 12 (1973), 157-176.
19. D. Lewis, Spaces on which each absolutely summing map is nuclear, Proc. Amer. Math. Soc. 31 (1972), 195-198.
20. Z. Nehari, On bounded bilinear forms, Ann. of Math. (2) 65 (1957), 153-162.
21. L. Page, Bounded and compact vectorial Hankel operators, Trans. Amer. Math. Soc. 150 (1970), 529-539.
22. S. Parrott, On a quotient norm and the Sz.-Nagy-Foias lifting theorem, J. Funct. Anal. 30 (1978), 311-328.
23. V. Paulsen, Every completely polynomially bounded operator is similar to a contraction, J. Funct. Anal. 55 (1984), 1-17.
24. V. Paulsen, Completely Bounded Maps and Dilations, Pitman Res. Notes Math. Ser. 146, Longman Scientific and Technical, Harlow, 1986.
25. V. Paulsen, The maximal operator space of a normed space, Proc. Edinburgh Math. Soc. (2) 39 (1996), 309-323.
26. G. Pisier, “Exact operator spaces” in Recent Advances in Operator Algebras (Orléans, 1992), Astérisque 232, Soc. Math. France, Montrouge, 1995, 159-186.
27. G. Pisier, The operator Hilbert space OH, complex interpolation and tensor norms, Mem. Amer. Math. Soc. 122 (1996), no. 585.
28. G. Pisier, A simple proof of a theorem of Kirchberg and related results on C* -norms, J. Operator Theory 35 (1996), 317-335.
29. G. Pisier, An introduction to the theory of operator spaces, preprint, 1997.
30. p -spaces and completely p -summing maps, Astérisque 247, Soc. Math. France, Montrouge, 1998.
31. Z.-J. Ruan, Subspaces of C* -algebras, J. Funct. Anal. 76 (1988), 217-230.
32. M. Takesaki, Theory of Operator Algebras, I, Springer-Verlag, New York, 1979.
33. G. Wittstock, Ein operatorwertiger Hahn-Banach Satz, J. Funct. Anal. 40 (1981), 127-150.