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Accueil > Pages web personnelles > Quanhua XU

Quanhua XU


Professor of Mathematics

Member of 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

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

 

 

Education

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

 

 

Academic Career

  • 1996-Present : Professor, Université de Franche-Comté
  • 1991-1996 : Senior Lecturer (Maître de conférences of First Class), Université Paris 6
  • 1989-1991 : Junior Lecturer (Maître de conférences), Université Lille 1

 

 

Selected scientific projects

  • 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 Lp-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 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 Lp-spaces, Operator spaces and Applications. BIRS (Banff). 27.06-02.07.2010 (with M. Junge and G. Pisier)
  • Workshop on Noncommutative Lp-spaces, Operator spaces and Applications. CIRM (Luminy). 08-12.06.2009 (with G. Pisier)
  • Workshop on Operator spaces, Noncommutative Lp-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

 

  • Bounds on the distance between a unital quantum channel and the convex hull of unitary channels, with applications to the asymptotic quantum Birkhoff conjecture (with R. Duan and N. Yu). Preprint.
  • 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 Lp-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 Lp-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 Lp-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 Lp-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 Lp-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 Cq and Rq into noncommutative Lp-spaces, 1≤ pMath. 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 Lp-spaces. Duke Math. J. 131 (2006), 525-574.
  • Maximality of subdiagonal algebras. J. Operator theory 54 (2005), 137-146.
  • A description of (Cp[Lp(M)], Rp [Lp(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 OLp structures of noncommutative Lp-spaces associated with hyperfinite von Neumann algebras (with M. Junge and Z-J. Ruan). Math. Scand. 96 (2005), 63-95.
  • COLp-spaces - the local structure of noncommutative Lp-spaces (with M. Junge, N.J. Nielsen and Z-J. Ruan). Adv. Math. 187 (2004), 257-319.
  • Noncommutative Lp-spaces (with G. Pisier). In Handbook of the Geometry of Banach Spaces, Vol. 2, 1459-1517. North-Holland, Amsterdam, 2003.
  • On subspaces of noncommutative Lp-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 Lp-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 Lp(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(Td)/H1(Dd). 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 vp (with G. Pisier). Springer Lect. Notes in Math. 1267 (1987), 185-209.