Exact operator spaces
Recent advances in operator algebras - Orléans, 1992, Astérisque, no. 232 (1995), pp. 159-186.
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author = {Pisier, Gilles},
title = {Exact operator spaces},
booktitle = {Recent advances in operator algebras - Orl\'eans, 1992},
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series = {Ast\'erisque},
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number = {232},
year = {1995},
zbl = {0844.46031},
mrnumber = {1372532},
language = {en},
url = {http://www.numdam.org/item/AST_1995__232__159_0/}
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Pisier, Gilles. Exact operator spaces, in Recent advances in operator algebras - Orléans, 1992, Astérisque, no. 232 (1995), pp. 159-186. http://www.numdam.org/item/AST_1995__232__159_0/

[AO] C. Akemann and P. Ostrand. Computing norms in group ${C}^{*}$-algebras. Amer. J. Math. 98 (1976), 1015-1047. | DOI | MR | Zbl

[B1] D. Blecher. Tensor products of operator spaces II. 1990. Canadian J. Math. 44 (1992) 75-90. | DOI | MR | Zbl

[B2] D. Blecher. The standard dual of an operator space. Pacific J. Math. 153 (1992) 15-30. | DOI | MR | Zbl

[BP] D. Blecher and V. Paulsen. Tensor products of operator spaces. J. Funct. Anal. 99 (1991) 262-292. | DOI | MR | Zbl

[DCH] J. De Cannière and U. Haagerup. Multipliers of the Fourier algebras of some simple Lie groups and their discrete subgroups. Amer. J. Math. 107 (1985), 455-500. | DOI | MR | Zbl

[EH] E. Effros and U. Haagerup. Lifting problems and local reflexivity for ${C}^{*}$-algebras. Duke Math. J. 52 (1985) 103-128. | DOI | MR | Zbl

[EKR] E. Effros J. Kraus and Z. J. Ruan. On two quantized tensor products. Preprint 1992. To appear. | MR | Zbl

[ER1] E. Effros and Z. J. Ruan. A new approach to operator spaces. Canadian Math. Bull. 34 (1991) 329-337. | DOI | MR | Zbl

[ER2] E. Effros and Z. J. Ruan. On the abstract characterization of operator spaces. Proc. Amer. Math. Soc. 119 (1993) 579-584. | DOI | MR | Zbl

[ER3] E. Effros and Z. J. Ruan. Self duality for the Haagerup tensor product and Hilbert space factorization. J. Funct. Anal. 100 (1991) 257-284. | DOI | MR | Zbl

[ER4] E. Effros and Z. J. Ruan. Recent development in operator spaces. Current topics in Operator algebras (edited by Araki, Choda, Nakagami, Saitô and Tomiyama). World Scientific, Singapore, 1991 p. 146-164. | MR | Zbl

[ER5] E. Effros and Z. J. Ruan. Mapping spaces and liftings for operator spaces. Proc. London Math. Soc. 69 (1994) 171-197. | DOI | MR | Zbl

[ER6] E. Effros and Z. J. Ruan. The Grothendieck-Pietsch and Dvoretzky-Rogers Theorems for operator spaces. J. Funct. Anal. 122 (1994) 428-450. | DOI | MR | Zbl

[ER7] E. Effros and Z. J. Ruan. On approximation properties for operator spaces, International J. Math. 1 (1990) 163-187. | DOI | MR | Zbl

[H] U. Haagerup. Injectivity and decomposition of completely bounded maps in "Operator algebras and their connection with Topology and Ergodic Theory". Springer Lecture Notes in Math. 1132 (1985) 170-222. | DOI | MR | Zbl

[HP] U. Haagerup and G. Pisier. Bounded linear operators between ${C}^{*}$-algebras. Duke Math. J. 71 (1993) 889-925. | DOI | MR | Zbl

[Hei] S. Heinrich. Ultraproducts in Banach space theory. J. für die reine und Angew. Math. 313 (1980) 72-104. | EuDML | MR | Zbl

[Her] R. Hernandez. Espaces ${L}^{p}$, factorisation et produits tensoriels dans les espaces de Banach. Comptes Rendus Acad. Sci. Paris Série A. 296 (1983) 385-388. | MR | Zbl

[J] M. Junge. Oral communication.

[JP] M. Junge and G. Pisier. Bilinear forms on exact operator spaces and $B\left(H\right)\otimes B\left(H\right)$. Geometric and Functional Analysis (GAFA), to appear. | MR | Zbl

[Ki] E. Kirchberg. On subalgebras of the CAR-algebra. J. Funct. Anal. (To appear) | MR | Zbl

[Kr] J. Kraus. The slice map problem and approximation properties. J. Funct. Anal. 102 (1991) 116-155. | DOI | MR | Zbl

[LR] J. Lindenstrauss and H. Rosenthal. The ${ℒ}_{p}$ spaces. Israel J. Math. 7 (1969) 325-349. | MR | Zbl

[Pa1] V. Paulsen. Completely bounded maps and dilations. Pitman Research Notes 146. Pitman Longman (Wiley) 1986. | MR | Zbl

[Pa2] V. Paulsen. Representation of Function algebras, Abstract operator spaces and Banach space Geometry. J. Funct. Anal. 109 (1992) 113-129. | DOI | MR | Zbl

[P1] G. Pisier. The operator Hilbert space $OH$, complex interpolation and tensor norms. To appear. | MR | Zbl

[P2] G. Pisier. Non-commutative vector valued ${L}_{p}$-spaces and completely $p$-summing maps. To appear. | MR | Zbl

[Ru] Z. J. Ruan. Subspaces of ${C}^{*}$-algebras. J. Funct. Anal. 76 (1988) 217-230. | DOI | MR | Zbl

[Sm] R. R. Smith. Completely bounded maps between ${C}^{*}$-algebras. J. London Math. Soc. 27 (1983) 157-166. | DOI | MR | Zbl

[Sz] A. Szankowski. $B\left(H\right)$ does not have the approximation property. Acta Math. 147 (1981) 89-108. | DOI | MR | Zbl

[Ta] M. Takesaki. Theory of Operator Algebras I. Springer-Verlag New-York 1979. | DOI | MR | Zbl

[W1] S. Wasserman. On tensor products of certain group ${C}^{*}$-algebras. J. Funct. Anal. 23 (1976) 239-254. | DOI | MR | Zbl

[W2] S. Wasserman. The slice map problem for ${C}^{*}$-algebras. Proc. London Math. Soc. 32 (1976) 537-559. | DOI | MR | Zbl