The "maximal" tensor product of operator spaces

Proceedings of the Edinburgh Mathematical Society

Volumn 42, Issue 2, 1999, Pages 267-284

  Oikhberg, Timur ^a   Pisier, Gilles ^b,c  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b TEXAS A AND M UNIVERSITY   (United States)

^c UNIVERSITÉ PARIS DESCARTES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22644448910     PISSN: 00130915     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0013091500020241     Document Type: Article

References (34)

1. D. BLECHER, Tensor products of operator spaces II, Canadian J. Math. 44 (1992), 75-90.
2. D. BLECHER, The standard dual of an operator space, Pacific J. Math. 153 (1992), 15-30.
3. D. BLECHER, A completely bounded characterization of operator algebras, Math. Ann. 303 (1995), 227-239.
4. D. BLECHER and V. PAULSEN, Tensor products of operator spaces, J. Funct. Anal. 99 (1991), 262-292.
5. D. BLECHER and V. PAULSEN, Explicit constructions of universal operator algebras and applications to polynomial factorization, Proc. Amer. Math. Soc. 112 (1991), 839-850.
6. D. BLECHER, Z. J. RUAN and A. SINCLAIR, A characterization of operator algebras, J. Funct. Anal. 89 (1990), 188-201.
7. D. BLECHER and R. SMITH, The dual of the Haagerup tensor product, J. London Math. Soc. 45 (1992), 126-144.
8. E. CHRISTENSEN, E. EFFROS and A. SINCLAIR, Completely bounded multilinear maps and C'-algebraic cohomology, Invent. Math. 90 (1987), 279-296.
9. E. CHRISTENSEN and A. SINCLAIR, Representations of completely bounded multilinear operators, J. Funct. Anal. 72 (1987), 151-181.
10. E. CHRISTENSEN and A. SINCLAIR, A survey of completely bounded operators, Bull. London Math. Soc. 21 (1989), 417-448.
11. P. DIXON, Varieties of Banach algebras, Quart. J. Math. Oxford 27 (1976), 481-487.
12. E. EFFROS and Z. J. RUAN, On approximation properties for operator spaces, Internat. J. Math. 1 (1990), 163-187.
13. E. EFFROS and Z. J. RUAN, A new approach to operator spaces, Canadian Math. Bull. 34 (1991), 329-337.
14. E. EFFROS and Z. J. RUAN, Self duality for the Haagerup tensor product and Hubert space factorization, J. Funct. Anal. 100 (1991), 257-284.
15. E. EFFROS and Z. J. RUAN, On the abstract characterization of operator spaces, Proc. Amer. Math. Soc. 119 (1993), 579-584.
16. E. EFFROS and Z. J. RUAN, Mapping spaces and liftings for operator spaces, Proc. London Math. Soc. 69 (1994), 171-197.
17. E. EFFROS and Z. J. RUAN, The Grothendieck-Pietsch and Dvoretzky-Rogers Theorems for operator spaces, J. Funct. Anal. 122 (1994), 428-450.
18. U. HAAGERUP and G. PISIER, Bounded linear operators between C-algebras, Duke Math. J. 71 (1993), 889-925.
19. M. JUNGE and G. PISIER, Bilinear forms on exact operator spaces and B(H) ⊗ B(H), Geom. Fund. Anal. 5 (1995), 329-363.
20. R. KADISON and J. RINGROSE, Fundamentals of the theory of operator algebras, II (Academic Press, New York, 1986).
21. E. KIRCHBERG, On non-semisplit extensions, tensor products and exactness of group Calgebras, Invent. Math. 112 (1993), 449-489.
22. T. OIKHBERG, Direct sums of homogeneous operator spaces, article in preparation.
23. V. PAULSEN, Completely bounded maps and dilations (Pitman Research Notes in Math. 146, Longman, Wiley, New York, 1986).
24. V. PAULSEN and S. POWER, Tensor products of non-self adjoint operator algebras, Rocky Mountain J. Math. 20 (1990), 331-350.
25. V. PAULSEN and R. SMITH, Multilinear maps and tensor norms on operator systems, J. Fund. Anal. 73 (1987), 258-276.
26. V. PESTOV, Operator spaces and residually finite-dimensional C-algebras, J. Fund. Anal. 123 (1994), 308-317.
27. G. PISIER, Factorization of linear operators and the Geometry of Banach spaces (CBMS (Regional conferences of the A.M.S.) 60, 1986), Reprinted with corrections 1987.
28. G. PISIER, The operator Hubert space OH, complex interpolation and tensor norms, Mem. Amer. Math. Soc. 122 585 (1996), 1-103.
29. G. PISIER, A simple proof of a theorem of Kirchberg and related results on C-norms, J. Operator Theory 35 (1996), 317-335.
30. G. PISIER, An introduction to the theory of operator spaces, preprint, to appear.
31. A. G. ROBERTSON, Injective matricial Hubert spaces, Math. Proc. Cambridge Philos. Soc. 110 (1991), 183-190.
32. Z. J. RUAN, Subspaces of C-algebras, J. Fund. Anal. 76 (1988), 217-230.
33. Z. J. RUAN, Injectivity and operator spaces, Trans. Amer. Math. Soc. 315 (1989), 89-104.
34. M. TAKESAKI, Theory of Operator Algebras I (Springer-Verlag, New York, 1979).