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Probably the most famous of Grothendieck's contributions to Banach space theory is the result that he himself described as "the fundamental theorem in the metric theory of tensor products".
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N. Tomczak-Jaegermann, On the Rademacher averages and the moduli of convexity and smoothness of the Schatten classes S p S_{p} , Studia Math. 50
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A. Pietsch, Operator Ideals , North-Holland Amsterdam, 1978
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G. Pisier, Grothendieck’s theorem for noncommutative C ∗ C^{*} -algebras, With an appendix on Grothendieck’s constants, J. Funct. Anal. 29
1978
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R.C. Blei, Multidimensional extensions of the Grothendieck inequality and applications, Ark. Mat. 17
1979
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U. Haagerup, An example of a non-nuclear C ∗ C^{*} -algebra which has the metric approximation property, Inventiones Mat. 50
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J.L. Krivine, Constantes de Grothendieck et fonctions de type positif sur les sphères, Adv. in Math. 31
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B.S. Tsirelson, Quantum generalizations of Bell’s inequality, Lett. Math. Phys. 4
1980
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M. Grötschel, L. Lovász and A. Schrijver, The ellipsoid method and its consequences in combinatorial optimization , Combinatorica 1
1981
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U. Haagerup, The best constants in the Khintchine inequality, Studia Math. 70
1982
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U. Haagerup, Solution of the similarity problem for cyclic representations of C ∗ C^{*} -algebras, Ann. Math. 118
1983
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U. Haagerup, All nuclear C ∗ C^{*} -algebras are amenable, Invent. Math. 74
1983
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M. Bożejko and G. Fendler, Herz–Schur multipliers and completely bounded multipliers of the Fourier algebra of a locally compact group, Boll. Unione Mat. Ital. (6) 3-A
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S. Kaijser and A.M. Sinclair, Projective tensor products of C ∗ C^{*} -algebras, Math. Scand. 55
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S.V. Kislyakov, Linear and complex analysis problem book, Section 6.5, Lecture Notes in Math. , 1043, Springer, Berlin, 1984
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A.M. Davie, Matrix norms related to Grothendieck’s inequality, Banach spaces (Columbia, MO, 1984) , 22–26, Lecture Notes in Math. , 1166, Springer, Berlin, 1985
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U. Haagerup, The Grothendieck inequality for bilinear forms on C ∗ C^{*} -algebras, Adv. Math. 56
1985
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J.P. Kahane, Some random series of functions, Second edition , Cambridge Studies in Advanced Mathematics, 5, Cambridge University Press, Cambridge, 1985
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L.A. Khalfin and B.S. Tsirelson, Quantum and quasiclassical analogs of Bell inequalities, Symposium on the Foundations of Modern Physics (Joensuu, 1985) , 441–460, World Sci. Publishing, Singapore, 1985
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J. Sawa, The best constant in the Khintchine inequality for complex Steinhaus variables, the case p = 1 p=1 , Studia Math. 81
1985
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G. Pisier, Factorization of operators through L p ∞ L_{p\infty} or L p 1 L_{p1} and noncommutative generalizations, Math. Ann. 276
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1987
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T. Itoh, On the completely bounded map of a C ∗ C^{*} -algebra to its dual space, Bull. London Math. Soc. 19
1987
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G. Pisier, The dual J ∗ J^{*} of the James space has cotype 2 2 and the Gordon–Lewis property, Math. Proc. Cambridge Philos. Soc. 103
1988
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H. König, On the complex Grothendieck constant in the n n -dimensional case, Geometry of Banach Spaces (Strobl, 1989) , 181–198, London Math. Soc. Lecture Note Ser., 158, Cambridge Univ. Press, Cambridge, 1990
1990
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1990
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Q. Xu, Applications du théorème de factorisation pour des fonctions à valeurs opérateurs, Studia Math. 95
1990
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V. Paulsen, Completely bounded maps and operator algebras , Cambridge University Press, Cambridge, 2002
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G. Pisier and D. Shlyakhtenko, Grothendieck’s theorem for operator spaces, Invent. Math. 150
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B. Kashin and S. Szarek, The Knaster problem and the geometry of high-dimensional cubes, C.R. Math. Acad. Sci. Paris 336
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E.G. Effros and Z.J. Ruan, A new approach to operator spaces, Canadian Math. Bull. 34
1991
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F. Lust-Piquard and G. Pisier, Noncommutative Khintchine and Paley inequalities, Ark. Mat. 29
1991
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C. Papadimitriou, and M. Yannakakis, Optimization, approximation, and complexity classes, J. Comput. System Sci. 43
1991
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J.A. Reeds, A new lower bound on the real grothendieck constant, unpublished note, 1991, available at http://www.dtc.umn.edu/reedsj/bound2.dvi
1991
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D. Blecher, Generalizing Grothendieck’s program, “Function spaces”, K. Jarosz (ed.), Lecture Notes in Pure and Applied Math., Vol. 136 , Marcel Dekker, 1992
1992
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S.V. Kislyakov, Absolutely summing operators on the disc algebra (Russian), Algebra i Analiz 3
1992
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F. Lust-Piquard, A Grothendieck factorization theorem on 2 2 -convex Schatten spaces, Israel J. Math. 79
1992
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G. Pisier, Interpolation between H p H^{p} spaces and noncommutative generalizations. I, Pacific J. Math. 155
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G. Pisier, Introduction to operator space theory , Cambridge University Press, Cambridge, 2003
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G. Pisier and Q. Xu, Non-commutative L p L^{p} -spaces, Handbook of the Geometry of Banach Spaces, Vol. 2 , 1459–1517, North-Holland, Amsterdam, 2003
2003
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M. Charikar and A. Wirth, Maximizing quadratic programs: extending Grothendieck’s inequality, FOCS (2004), 54–60
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N. Ozawa, About the QWEP conjecture, Internat. J. Math. 15
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F. Rădulescu, A comparison between the max and min norms on C ∗ ( F n ) ⊗ C ∗ ( F n ) C^{*}(F_{n})\otimes C^{*}(F_{n}) , J. Operator Theory 51
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N.J. Kalton, Rademacher series and decoupling, New York J. Math. 11
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A. Peralta, New advances on the Grothendieck’s inequality problem for bilinear forms on JB*-triples, Math. Inequal. Appl. 8
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N. Alon and E. Berger, The Grothendieck constant of random and pseudo-random graphs, Discrete Optim. 5
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N.P. Brown and N. Ozawa, C ∗ C^{*} -algebras and finite-dimensional approximations , Graduate Studies in Mathematics, 88, American Mathematical Society, Providence, RI, 2008
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J. Diestel, J.H. Fourie and J. Swart, The metric theory of tensor products. Grothendieck’s résumé revisited , American Mathematical Society, Providence, RI, 2008
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D. Pérez-García, M.M. Wolf, C. Palazuelos, I. Villanueva, and M. Junge, Unbounded violation of tripartite Bell inequalities, Comm. Math. Phys. 279
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U. Haagerup and M. Musat, The Effros–Ruan conjecture for bilinear forms on C ∗ C^{*} -algebras, Invent. Math. 174
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M. Junge and J. Parcet, Rosenthal’s theorem for subspaces of noncommutative L p L_{p} , Duke Math. J. 141
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G. Pisier, Remarks on the non-commutative Khintchine inequalities for 0 < p < 2 0<p<2 , J. Funct. Anal. 256
2009
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P. Raghavendra and D. Steurer, Towards computing the Grothendieck constant. Proceedings of SODA. 2009, 525-534
2009
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M. Junge and J. Parcet, Maurey’s factorization theory for operator spaces, Math. Ann. 347
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M. Junge and J. Parcet, Mixed-norm inequalities and operator space L p L_{p} embedding theory, Mem. Amer. Math. Soc. 203
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M. Junge, and Q. Xu, Representation of certain homogeneous Hilbertian operator spaces and applications, Invent. Math. 179
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2011
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