Professor of Mathematics

Senior Member of IUF -
Institut Universitaire de France

Address

 Laboratoire de Mathématiques (UMR 6623)
 Université de Franche-Comté
 25 030 Besançon cedex - France
 Phone : + 33 (0)3 81 66 63 99
 Fax : + 33 (0)3 81 66 66 23
 email : qxu univ-fcomte.fr

 
Research interests

• Noncommutative analysis
• Operator spaces
• Quantum probability
• Noncommutative/classical martingale inequalities
• Noncommutative/classical harmonic analysis
• Noncommutative L_p-spaces
• Geometry of Banach spaces

Education

• 1993 : Habilitation, Université Paris 6 Pierre et Marie Curie
• 1988 : PhD, Université Paris 6 ; Adviser : Gilles PISIER
• 1985 and 1982 : Master and BS in Mathematics, Wuhan University

Academic Career

• 2014 : Senior Member of Institut Universitaire de France
• 1996-Present : Professor, Université de Franche-Comté
  (PR1 en 2003, PREX1 en 2008, PREX2 en 2014, promotions par CNU)
• 1991-1996 : Senior Lecturer (Maître de conférences de première classe), Université Paris 6
• 1989-1991 : Junior Lecturer (Maître de conférences), Université Lille 1

Selected scientific projects

• Leader (porteur de projet) : ANR PRC Générique “Noncommutative analysis on groups and quantum groups”, 2020-2023.

• Leader (porteur de projet) : ANR Programme Blanc “Interactions between operator space theory and quantum probability with applications to quantum information”, 2011-2015.

• Leader (porteur de projet) : ANR Programme Blanc “Noncommutative L_p-spaces, Quantum Probability, Operator Spaces and Applications”, 2007-2010.

• Leader (porteur de projet) : French Government Programme ACI Jeunes (the former ANR Jeunes) “Quantum Probability, Operator Spaces and Applications”, 2000-2002.

• Leader : Cooperation programme between CNRS and University of Illinois at Urbana-Champaign on “Operator Spaces, Operator Algebras, Noncommutative Probability and Locally Compact Quantum Groups”, 2004-2006. The American leader : Marius Junge.

• Leader : European bilateral Project Polonium “Noncommutative Probability and Operator Space Theory” between Besançon and Wroclaw, 2000-2002

Selected conference organizations

• Conference on Analysis on Groups and Quantum groups, Besançon. 18-21.12.2024. (with U. Franz, Y. Kuznetsova, C. Le Merdy, A. Nou).

• Conference on Interactions between Noncommutative Analysis and Quantum Information Theory, Harbin, 31.05-05.06.2019 (with K. Li, Z. Wang, J. Wu and Z. Yin).

• Workshop on Banach Space Theory and Applications, TSIMF, Sanya. 27-31.08.2018 (with S. Bu and L. Cheng).

• IWOTA Special Session on Operator Spaces and Harmonic Analysis, Shanghai, 23-27.07.2018 (with G. Hong and Z-J. Ruan).

• Workshop on Interactions between Operator Space Theory and Quantum Probability with Applications to Quantum Information. Oberwolfach, 06-12.05.2018 (with U. Franz, M. Junge and G.Pisier).

• Workshop on Operator Algebras and Quantum Information Theory. Institut Henri Poincaré, Paris, 11-15.09.2017 (with B. Collins and M. Junge).
  See also the special trimester on Analysis in Quantum Information Theory, Institut Henri Poincaré, Paris, 04.09-15.12.2017.

• Symposium on Modern Analysis and Applications. Harbin, 18-21.07.2016.

• Workshop on Operator Spaces, Quantum Probability and Quantum Information. Wuhan, 05-07.06.2015.

• Conference on Operator Spaces and Quantum Probability. Besançon. 15-19.12.2014.

• Conference on Banach Space Methods in Noncommutative Geometry. Wuhan University. 08-13.06.2014 (with E. Germain, M.P. Gomez Aparicio, P-Y. Le Gall, Y-J. Yao and G. Yu).

• Conference on Operator Spaces, Quantum Probability and Applications. Wuhan University. 05-09.06.2012 (with T. Ma and M. Wang).

• Workshop on Noncommutative L_p-Spaces, Operator Spaces and Applications. BIRS (Banff). 27.06-02.07.2010 (with M. Junge and G. Pisier).

• Workshop on Noncommutative L_p-spaces, Operator Spaces and Applications. CIRM (Luminy). 08-12.06.2009 (with G. Pisier).

• Workshop on Operator Spaces, Noncommutative L_p-Spaces and Applications. CIRM (Luminy). 25-29.06.2007 (with G. Pisier).

• Workshop on Operator Spaces, Operator Algebras and Noncommutative Probability. Besançon. 06-10.06.2005 (with C. Le Merdy and E. Ricard).

• Workshop on Noncommutative Martingale Inequalities and Free probability. Greifswald. 15-20.06.2003 (with M. Bozejko).

Publications
 

• Holomorphic functional calculus and vector-valued Littlewood-Paley-Stein theory for semigroups. J. Eur. Math. Soc. Online (2024).

• Atomic decompositions for noncommutative martingales (with Z. Chen and N. Randrianantoanina). J. Funct. Anal. 284 (2023), no. 9, Paper No. 109877, 47 pp.

• Optimal orders of the best constants in the Littlewood-Paley inequalities. J. Funct. Anal. 283 (2022), no. 6, Paper No. 109570, 37 pp.

• A Hörmander-Mikhlin multiplier theory for free groups and amalgamated free products of von Neumann algebras (with T. Mei and E. Ricard). Adv. Math. 403 (2022), Paper No. 108394, 32 pp.

• Notes on real interpolation of operator L_p (with M. Junge). Acta math. Scientia. 41 (2021), 2173-2182.

• Vector-valued Littlewood-Paley-Stein Theory for Semigroups II. Int. Math. Res. Not. 21 (2020), 7769-7791.

• Noncommutative Davis type decompositions and applications (with N. Randrianantoanina and L. Wu). J. London Math. Soc. 99 (2019), 97-126.

• Weighted variation inequalities for differential operators and singular integrals in higher dimensions (with T. Ma and J. L. Torrea). Science China Math. 60 ( 2017), 1419-1442.

• Bounds on the distance between a unital quantum channel and the convex hull of unitary channels (with R. Duan and N. Yu). IEEE Transactions on Information Theory 63 (2017), 1299-1310.

• Characterizations of operator-valued Hardy spaces and applications to harmonic analysis on quantum tori (with R. Xia and X. Xiong).
  Adv. Math. 291 (2016), 183-227.

• Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori (with X. Xiong and Z. Yin). Memoirs Amer. Math. Soc. 252 (2018), no. 1203, vi+118 pp. See also C. R. Math. Acad. Sci. Paris. 353 (2015), 729-734.

• A noncommutative martingale convexity inequality (with E. Ricard). Ann. Probab. T44 (2016), 867-882.

• Weighted variation inequalities for differential operators and singular integrals (with T. Ma and J. L. Torrea). J. Funct. Anal. 265 (2013), 545-561.

• A Helson-Szegö theorem for subdiagonal subalgebras with applications to Toeplitz operators (with L. E. Labuschagne).
  J. Funct. Anal. 265 (2013), 545-561.

• H∞ functional calculus and maximal inequalities for vector-valued semigroups of contractions on L_p-spaces. Int. Math. Res. Not. 14 (2015), 5715-5732.

• On the growth of vector-valued Fourier series (with J. Parcet and F. Soria). Indiana Math. J. 62 (2013), 1765-1784.

• Harmonic analysis on quantum tori (with Z. Chen and Z. Yin). Comm. Math. Phys. 322 (2013), 755-805.

• Strong q-variation inequalities for analytic semigroups (with C. Le Merdy). Ann. Inst. Fourier. 62 (2012), 2069-2097.

• Maximal theorems and square functions for analytic operators on L_p-spaces (with C. Le Merdy). J. London Math. Soc. 86 (2012), 343-365.

• On the vector-valued Littlewood-Paley-Rubio de Francia inequality (with D. Potapov and F.Sukochev). Revista Mat. Iberoa. 28 (2012), 839-856.

• Complex interpolation of weighted noncommutative L_p-spaces (with E. Ricard). Houston J. Math. 37 (2011), 1165-1179.

• Representation of certain homogeneous Hilbertian operator spaces and applications (with M. Junge). Invent. Math.179 (2010), 75-118.

• A reduction method for noncommutative L_p-spaces and applications (with U. Haagerup and M. Junge). Trans. Amer. Math. Soc. 362 (2010), 2125-2165.

• BMO functions and Carleson measures in uniformly convex spaces (with C. Ouyang). Canadian J. Math. 62 (2010), 827-844.

• Introduction to operator algebras and noncommutative L_p-spaces (with T. N. Bekjan and Z. Chen ; in Chinese). Science Press (China). 2010 ; vi +194 pages.

• Interactions between quantum probability and operator spaces. Lectures at International Spring School “Quantum Potential Theory”. Editors : U. Franz and M. Schürman. Springer Lect. Notes in Math. 2008 ; 1954 ; 117-159.

• Noncommutative Burkholder/Rosenthal inequalities II : Applications (with M. Junge). Israel J. Math. 167 (2008), 227-282.

• Riesz and Szegö type factorizations for noncommutative Hardy spaces (with T. N. Bekjan). J. Operator Theory. 62 (2009), 215-231.

• The little Grothendieck theorem and Khintchine inequalities for symmetric spaces of measurable operators (with F. Lust-Piquard). J. Funct. Anal. 244 (2007), 488-503.

• Rosenthal type inequalities for free chaos (with M. Junge and J. Parcet). Ann. Proba. 35 (2007), 1374-1437.

• H∞ functional calculus and square functions on noncommutative L_p-spaces (with M. Junge and C. Le Merdy). Astérisque. Vol. 305, 2006. vi+138 pages. See also C. R. Math. Acad. Sci. Paris. 337 (2003), 93-98.

• Noncommutative maximal ergodic inequalities (with M. Junge). J. Amer. Math. Soc. 20 (2007), 385-439. See also C. R. Acad. Sci. Paris. 334 (2002), 773-778.

• Khintichine type inequalities for reduced free products and applications (with E. Ricard). J. Reine Angew. Math. 599 (2006), 27-59.

• Characterization of multiqubit pure-state entanglement (with Z. Chen). Phys.Rev. A. 73 (034306):1-3, 2006.

• Embedding of C_q and R_q into noncommutative L_p-spaces, 1≤ p<q≤ 2. Math. Ann. 335 (2006), 109-131.

• Vector-valued Littlewood-Paley-Stein theory for semigroups (with T. Martinez and J. L. Torrea). Adv. Math. 203 (2006), 430-475.

• Operator space Grothendieck inequalities for noncommutative L_p-spaces. Duke Math. J. 131 (2006), 525-574.

• Maximality of subdiagonal algebras. J. Operator theory 54 (2005), 137-146.

• A description of (C_p(L_p(M)), R_p (L_p(M)))_θ. Proc. Edinburgh Math. Soc. 135 (2005), 1073-1083.

• On the best constants in some noncommuttive martingale inequalities (with M. Junge). Bull. London Math. Soc. 37 (2005), 243-253.

• Rigid OL_p structures of noncommutative L_p-spaces associated with hyperfinite von Neumann algebras (with M. Junge and Z-J. Ruan). Math. Scand. 96 (2005), 63-95.

• COL_p-spaces - the local structure of noncommutative L_p-spaces (with M. Junge, N.J. Nielsen and Z-J. Ruan). Adv. Math. 187 (2004), 257-319.

• Noncommutative L_p-spaces (with G. Pisier). In Handbook of the Geometry of Banach Spaces, Vol. 2, 1459-1517. North-Holland, Amsterdam, 2003.

• On subspaces of noncommutative L_p-spaces (with Y. Raynaud). J. Funct. Anal. 203 (2003), 149-196. See also C. R. Acad. Sci. Paris. 333 (2001), 213-218.

• Embedding of noncommutative L_p-spaces : p < 1 (with F.A. Sukochev). Arch. Math. 80 (2003), 151-164.

• Noncommutative Burkholder/Rosenthal inequalities (with M. Junge). Ann. Probab. 31 (2003), 948-995.

• Remarks on interacting Fock spaces. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 3 (2000), 191–198.

• Interpolation of Schur multiplier spaces. Math. Z. 235 (2000), 707–715.

• Partial retractions for weighted Hardy spaces (with S. Kisliakov). Studia Math. 138 (2000), 251-264.

• Brownian martingales and some new results on interpolation of Hardy spaces. Potential Anal. 11 (1999), 257-278.

• Littlewood-Paley theory for functions with values in uniformly convex spaces. J. Reine Angew. Math. 504 (1998), 195-226.

• Noncommutative martingale inequalities (with G. Pisier). Comm. Math. Phys. 189 (1997), 667-698. See also C. R. Acad. Sci. Paris. 323 (1996), 817-822.

• Fourier multipliers for L_p(Rⁿ) via q-variation. Pacific J. Math.176 (1996), 287-296.

• Real interpolation and singular integrals (with S. Kisliakov). St. Petersburg Math. J. 8 (1996), 75-109.

• Interpolation of operator spaces. J. Funct. Anal. 139 (1996), 500-539.

• Some results related to interpolation on Hardy spaces of regular martingales. Israel J. Math. 91(1995), 173-187.

• Interpolation of weighted and vector-valued Hardy spaces (with S. Kisliakov). Trans. Amer.Math. Soc. 343 (1994), 1-34. See also C. R. Acad. Sci. Paris. 313 (1991), 249-254.

• Monotonicity between vector-valued bounded sequence spaces (with M. Mastylo). Bull. Polish Acad. Sci. Math. 41 (1993), 177-187.

• Some properties of the quotient space L₁(T^d)/H₁(D^d). Illinois J. Math. 37 (1993), 437-454.

• Notes on interpolation of Hardy spaces. Ann. Inst. Fourier, 42 (1992), 875-889. Erratum : 43 (1993), 56.

• Real interpolation of some Banach lattices valued Hardy spaces. Bull. Sci. Math. 116 (1992), 227-246.

• Radon-Nikodym property in symmetric spaces of measurable operators. Proc. Amer. Math. Soc. 115 (1992), 329-335.

• Interpolation between vector-valued Hardy spaces (with O. Blasco). J. Funct. Anal. 102 (1991), 331-359.

• Analytic functions with values in lattices and symmetric spaces of measurable operators. Math. Proc. Cambridge Philos. Soc. 109 (1991), 541-563.

• Applications du théorème de factorisation pour des fonctions à valeurs opérateurs. Studia Math. 95 (1990), 273-292.

• Convexités uniformes et inégalités de martingales. Math. Ann. 287 (1990), 193-211.

• Convexité uniforme des espaces symétriques d’opérateurs mesurables. C. R. Acad. Sci. Paris. 309 (1989), 251-254.

• Espaces d’interpolation réels entre les espaces Vp : propriétés géométriques et applications probabilistes. Séminaire d’Analyse Fonctionelle 1985/1986/1987, Vol. 28, pp. 77-123, 1988. Publ.Math. Univ. Paris VII.

• Inégalités pour les martingales de Hardy et renormage des espaces quasi-normés. C. R. Acad. Sci. Paris. 306 (1988), 601-604.

• The strong p-variation of martingales and orthogonal series (with G. Pisier). Probab. Theory Related Fields, 77 (1988), 497-514.

• Cotype of the space (A₀, A₁) _θ,1. Springer Lect. Notes in Math. 1267 (1987), 210-212.

• Random series in the real interpolation spaces between the spaces v_p (with G. Pisier). Springer Lect. Notes in Math. 1267 (1987), 185-209.

• On representations of families of distributions. Acta Math. Sinica 30 (1987), 713-720.

• The type of entire functions of proximate order (R) defined by Dirichlet series.Chinese Ann. Math. Ser. A 7 (1986), 266-277.

• Degrees of nearness. Acta Math. Sci. 5 (1985), 243-250.

• On singularities of analytic functions. J. Wuhan Univ. Natur. Sci. Ed. 3 (1985), 29-40.