Espaces d'opérateurs : une nouvelle dualité

Séminaire Bourbaki : volume 1995/96, exposés 805-819, Astérisque, no. 241 (1997), Exposé no. 814, 30 p.

EuDML 110216 | MR 1472542 | Zbl 0924.46044 | 1 citation dans Numdam

@incollection{SB_1995-1996__38__243_0,
     author = {Pisier, Gilles},
     title = {Espaces d'op\'erateurs : une nouvelle dualit\'e},
     booktitle = {S\'eminaire Bourbaki : volume 1995/96, expos\'es 805-819},
     author = {Collectif},
     series = {Ast\'erisque},
     note = {talk:814},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {241},
     year = {1997},
     zbl = {0924.46044},
     mrnumber = {1472542},
     language = {fr},
     url = {archive.numdam.org/item/SB_1995-1996__38__243_0/}
}

Pisier, Gilles. Espaces d'opérateurs : une nouvelle dualité, dans Séminaire Bourbaki : volume 1995/96, exposés 805-819, Astérisque, no. 241 (1997), Exposé no. 814, 30 p. http://archive.numdam.org/item/SB_1995-1996__38__243_0/

Bibliographie

[A] C. Anantharaman-Delaroche - Classification des $C^{*}$ -algèbres purement infinies nucléaires (d'après E. Kirchberg), Sém. Bourbaki, novembre 1995, 48ème année, 1995-96, n° 805. | EuDML 110224 | Numdam | MR 1472533 | Zbl 0961.46040

[BL] J. Bergh and J. Löfström - Interpolation spaces. An introduction, Springer-Verlag, New York, 1976. | MR 482275 | Zbl 0344.46071

[B1] D. Blecher - Tensor products of operator spaces II, Canadian J. Math. 44 (1992), 75-90. | Article | MR 1152667 | Zbl 0787.46059

[B2] D. Blecher - The standard dual of an operator space, Pacific J. Math. 153 (1992), 15-30. | Article | MR 1145913 | Zbl 0726.47030

[B3] D. Blecher - A completely bounded characterization of operator algebras, Math. Ann. 303 (1995), 227-240. | Article | EuDML 165366 | MR 1348798 | Zbl 0892.47048

[BLM] D. Blecher and C. Le Merdy - On quotients of function algebras and operator algebra structures on $ℓ_{p}$ , à paraître. | Zbl 0854.47029

[BP1] D. Blecher and V. Paulsen - Tensor products of operator spaces, J. Funct. Anal. 99 (1991), 262-292. | Article | MR 1121615 | Zbl 0786.46056

[BP2] D. Blecher and V. Paulsen - Explicit constructions of universal operator algebras and applications to polynomial factorization, Proc. Amer. Math. Soc. 112 (1991), 839-850. | Article | MR 1049839 | Zbl 0767.46037

[BRS] D. Blecher, Z. J. Ruan and A. Sinclair - A characterization of operator algebras, J. Funct. Anal. 89 (1990), 188-201. | Article | MR 1040962 | Zbl 0714.46043

[Ca] T. K. Carne - Not all $H'$ -algebras are operator algebras, Proc. Camb. Phil. Soc. 86 (1979), 243-249. | Article | MR 538746 | Zbl 0409.46066

[CE] M. D. Choi and E. Effros - Injectivity and operator spaces, J. Funct. Anal. 24 (1977), 156-209. | Article | MR 430809 | Zbl 0341.46049

[CES] E. Christensen, E. Effros and A. Sinclair - Completely bounded multilinear maps and $C^{*}$ -algebraic cohomology, Invent. Math. 90 (1987), 279-296. | Article | EuDML 143510 | MR 910202 | Zbl 0646.46052

[CS] E. Christensen and A. Sinclair - A survey of completely bounded operators, Bull. London Math. Soc. 21 (1989), 417-448. | Article | MR 1005819 | Zbl 0698.46044

[CV] Y. Colin De Verdière - Distribution de points sur une sphère (d'après Lubotzky, Phillips et Sarnak), Sém. Bourbaki, exposé n° 703, nov. 1989, Astérisque, 177-178 (1989), 83-93. | EuDML 110118 | Numdam | MR 1040569 | Zbl 0701.11024

[EH] E. Effros and U. Haagerup - Lifting problems and local reflexivity for $C^{*}$ - algebras, Duke Math. J. 52 (1985), 103-128. | Article | MR 791294 | Zbl 0613.46047

[EK] E. Effros and A. Kishimoto - Module maps and Hochschild-Johnson cohomology, Ind. Univ. Mah. J. 36 (1987), 257-276. | Article | MR 891774 | Zbl 0635.46062

[ER1] E. Effros and Z. J. Ruan - A new approach to operator spaces, Canadian Math. Bull. 34 (1991), 329-337. | Article | MR 1127754 | Zbl 0769.46037

[ER2] E. Effros and Z. J. Ruan - On the abstract characterization of operator spaces, Proc. Amer. Math. Soc. 119 (1993), 579-584. | Article | MR 1163332 | Zbl 0808.46026

[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. | Article | MR 1125226 | Zbl 0761.47022

[ER4] E. Effros and Z. J. Ruan - Mapping spaces and liftings for operator spaces, Proc. London Math. Soc. 69 (1994), 171-197. | Article | MR 1272425 | Zbl 0814.47053

[ER5] E. Effros and Z. J. Ruan - The Grothendieck-Pietsch and Dvoretzky-Rogers theorems for operator spaces, J. Funct. Anal. 122 (1994) 428-450. | Article | MR 1276165 | Zbl 0802.46014

[ER6] E. Effros and Z. J. Ruan - On approximation properties for operator spaces, International J. Math. 1, (1990), 163-187. | Article | MR 1060634 | Zbl 0747.46014

[EW] E. Effros and S. Winkler - Matrix convexity : operator analogues of the bipolar and Hahn-Banach theorems. Preprint, 1995. | MR 1430718 | Zbl 0897.46046

[G] A. Grothendieck - Résumé de la théorie métrique des produits tensoriels topologiques, Boll. Soc. Mat. São-Paulo 8 (1956), 1-79. | MR 94682 | Zbl 0074.32303

[H] U. Haagerup - Decomposition of completely bounded maps on operator algebras, manuscrit non publié, Sept. 1980.

[JP] M. Junge and G. Pisier - Bilinear forms on exact operator spaces and $B (H) \otimes B (H)$ , Geometric and Functional Analysis (GAFA Journal) 5 (1995), 329-363. | Article | EuDML 58192 | Zbl 0832.46052

[Ki1] E. Kirchberg - On non-semisplit extensions, tensor products and exactness of group $C^{*}$ -algebras, Invent. Math. 112 (1993), 449-489. | Article | EuDML 144111 | MR 1218321 | Zbl 0803.46071

[Ki2] E. Kirchberg - Commutants of unitaries in $U H F$ algebras and functorial properties of exactness, J. reine angew. Math. 452 (1994), 39-77. | EuDML 153631 | MR 1282196 | Zbl 0796.46043

[LeM1] C. Le Merdy - On the duality of operator spaces, Canad. Math. Bull. 38 (1995), 334-346. | Article | MR 1347307 | Zbl 0838.46046

[LeM2] C. Le Merdy - Representations of a quotient of a subalgebra of $B (X)$ . Math. Proc. Cambridge Phil. Soc. 119 (1996), 83-90. | Article | MR 1356160 | Zbl 0847.46029

[LPS] A. Lubotzky, R. Phillips and P. Sarnak - Hecke operators and distributing points on $S^{2}$ , I, Comm. Pure and Applied Math. 39 (1986), 149-186. | Article | MR 861487 | Zbl 0619.10052

[Pa1] V. Paulsen - Completely bounded maps and dilations, Pitman Research Notes 146, Pitman Longman (Wiley) 1986. | MR 868472 | Zbl 0614.47006

[Pa2] V. Paulsen - Representation of function algebras, abstract operator spaces and Banach space geometry, J. Funct. Anal. 109 (1992), 113-129. | Article | MR 1183607 | Zbl 0796.46038

[Pa3] V. Paulsen - Completely bounded maps on $C^{*}$ -algebras and invariant operator ranges, Proc. Amer. Math. Soc. 86 (1982), 91-96. | MR 663874 | Zbl 0554.46028

[PS] V. Paulsen and R. Smith - Multilinear maps and tensor norms on operator systems, J. Funct. Anal. 73 (1987), 258-276. | Article | MR 899651 | Zbl 0644.46037

[P1] G. Pisier - The operator Hilbert space $O H$ , complex interpolation and tensor norms, Memoirs Amer. Math. Soc. (1996), à paraître. | MR 1342022 | Zbl 0932.46046

[P2] G. Pisier - Espaces de Banach quantiques : Une introduction à la théorie des espaces d'opérateurs (59 p.), Journée de la S. M. F., 1994, Soc. Math. France. | MR 1465454 | Zbl 0947.46039

[P3] G. Pisier - Exact operator spaces, Colloque sur les algèbres d'opérateurs. (Orléans 1992), Astérisque 232, Soc. Math. France (1995), 159-187. | MR 1372532 | Zbl 0844.46031

[P4] G. Pisier - Non-commutative vector valued $L_{p}$ -spaces and completely $p$ -summing maps, à paraître probablement dans Astérisque. | MR 1648908 | Zbl 0937.46056

[P5] G. Pisier - An introduction to the theory of operator spaces. En préparation. | Article

[P6] G. Pisier - Similarity problems and completely bounded maps, Springer Lecture notes 1618 (1995), Springer verlag, Heidelberg. | MR 1818047 | Zbl 0843.47010

[Ru1] Z. J. Ruan - Subspaces of $C^{*}$ -algebras, J. Funct. Anal. 76 (1988), 217-230. | Article | MR 923053 | Zbl 0646.46055

[Sk] G. Skandalis - Algèbres de von Neumann de groupes libres and probabilités non commutatives, Sém. Bourbaki, exposé n° 764, nov. 1992, Astérisque 216 (1993),87-102. | EuDML 110180 | Numdam | MR 1246394 | Zbl 0797.46042

[Va] A. Valette - An application of Ramanujan graphs to $C^{*}$ -algebra tensor products, à paraître. | Numdam | Zbl 0874.46038

[V1] N. Varopoulos - A theorem on operator algebras, Math. Scand. 37 (1975), 173-182. | Article | EuDML 166438 | MR 397436 | Zbl 0337.46041

[Vo] D. Voiculescu - Property $T$ and approximation of operators, Bull. London Math. Soc. 22 (1990), 25-30. | Article | MR 1026768 | Zbl 0718.46023

[Wa1] S. Wassermann - On tensor products of certain group $C^{*}$ -algebras, J. Funct. Anal. 23 (1976), 239-254. | Article | MR 425628 | Zbl 0358.46040

[Wa2] S. Wassermann - Exact $C^{*}$ -algebras and related topics, Lecture Notes Series, Seoul Nat. Univ. (1994). | MR 1271145 | Zbl 0828.46054

[Wi] G. Wittstock - Ein operatorwertigen Hahn-Banach Satz, J. Funct. Anal. 40 (1981), 127-150. | Article | MR 609438 | Zbl 0495.46005

[X] Q. Xu - The real interpolation in the category of operator spaces, J. Funct. Anal., à paraître.