H∞ functional calculus and square functions on noncommutative Lp-spaces

Asterisque

Volumn , Issue 305, 2006, Pages 1-138

  Junge, Marius ^a   Le Merdy, Christian ^b   Xu, Quanhua ^b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b UNIVERSITÉ DE FRANCHE COMTÉ   (France)

Author keywords

Completely bounded maps; Diffusion semigroups; H functional calculus; Multipliers; Noncommutative L p spaces; Sectorial operators; Square functions

Indexed keywords

EID: 33947137719     PISSN: 03031179     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Article

References (80)

1. p-spaces, Canad. J. Math. 27 (1975), p. 1075-1082.
2. p spaces, Canad. Math. Bull 20 (1977), p. 285-292.
3. D. ALBRECHT, X. T. DUONG & A. MCINTOSH - Operator theory and harmonic analysis, in Instructional Workshop on Analysis and Geometry, Part III (Canberra, 1995), Proc. Centre Math. Appl. Austral. Nat. Univ., vol. 34, Austral. Nat. Univ., 1996, p. 77-136.
4. C. ANANTHARAMAN-DELAROCHE - On ergodic theorems for free group actions on noncommutative spaces, Probab. Theory Related Fields 135 (2006), p. 520-546.
5. P. AUSCHER, A. MCINTOSH & A. NAHMOD - Holomorphic functional calculi of operators, quadratic estimates and interpolation, Indiana Univ. Math. J. 46 (1997), p. 375-403.
6. J. BERGH & J. LÖFSTRÖM - Interpolation spaces, Springer-Verlag, 1970.
7. E. BERKSON & T. A. GILLESPIE - Spectral decompositions and harmonic analysis on UMD Banach spaces, Studia Math. 112 (1994), p. 13-49.
8. E. BERKSON, T. A. GILLESPIE & P. S. MUHLY - Abstract spectral decompositions guaranteed by the Hilbert transform, Proc. London Math. Soc. 53 (1986), p. 489-517.
9. P. BIANE - Free hypercontractivity, Commun. Math. Phys. 184 (1997), p. 457-474.
10. E. BLANCHARD & K. DYKEMA - Ernbeddings of reduced free products of operator algebras, Pacific J. Math. 199 (2001), p. 1-19.
11. M. BOŻEJKO - Ultracontractivity and strong Sobolev inequality for q-Ornstein-Uhlenbeck semigroup, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 2 (1999), p. 203-220.
12. M. BOŻEJKO & G. FENDLER - A note on certain partial sum operates, 2005, Preprint.
13. M. BOŻEJKO, B. KÜMMERER & R. SPEICHER - q-Gaussian processes: non-commutative and classical aspects, Commun. Math. Phys. 185 (1997), p. 129-154.
14. M. BOŻEJKO & R. SPEICHER - An example of a generalized brownian motion, Commun. Math. Phys. 137 (1991), p. 519-531.
15. _, Completely positive maps on Coxeter groups, deformed commutation relations, and operator spaces, Math. Ann. 300 (1994), p. 97-120.
16. O. BRATELLI & D. W. ROBINSON - Operator algebras and quantum statistical mechanics II, Springer-Verlag, 1981.
17. D. BURKHOLDER - Martingales and singular integrals in Banach spaces, in Handbook of the Geometry of Banach Spaces, Vol. I (W. B. Johnson & J. Lindenstrauss, eds.), Elsevier, 2001, p. 233-269.
18. M.-D. CHOI - A schwarz inequality for positive linear maps on C*-algebras, Illinois J. Math. 18 (1974), p. 565-588.
19. P. CLÉMENT, B. DE PAGTER, F. SUKOCHEV & H. WITVLIET - Schauder decompositions and multiplier theorems, Studia Math. 138 (2000), p. 135-163.
20. M. COWLING - Harmonic analysis on semigroups, Ann. of Math. 117 (1983), p. 267-283.
21. ∞ functional calculus, J. Austral. Math. Soc. Ser. A 60 (1996), p. 51-89.
22. E. B. DAVIES - One-parameter semigroups, London Math. Soc. Monographs, vol. 15, Academic Press Inc., 1980.
23. J. DIESTEL & J. J. UHL - Vector measures, vol. 15, Amer. Math. Soc., 1977, préface de J. Pettis, Mathematical Surveys no. 15.
24. p-spaces, Proc. Centre Math. Appl. Austral. Nat. Univ., vol. 24, Austral. Nat. Univ., 1989, p. 91-102.
25. p-spaces, J. Operator Theory 7 (1987), p. 255-279.
26. T. FACK & H. KOSAKI - Generalized s-numbers of τ-measurable operators, Pacific J. Math. 123 (1986), p. 269-300.
27. p-spaces, Canad. J. Math. 49 (1997), p. 736-748.
28. J. B. GARNETT - Bounded analytic functions, Pure Appl. Math., Academic Press Inc., 1981.
29. J. A. GOLDSTEIN - Semigroups of linear operators and applications, Oxford University Press, 1985.
30. U. HAAGERUP - An example of a non nuclear C*-algebra, which has the metric approximation property, Invent. Math. 50 (1979), p. 279-293.
31. p and non-commutative Λ(p)-sets, Studia Math. 137 (1999), p. 203-260.
32. p-spaces via the transference principle, Adv. Differential Equations 3 (1998), p. 847-872.
33. M. JUNGE - Doob's inequality for non-commutative martingales, J. Reine Angew. Math. 549 (2002), p. 149-190.
34. p non commutatifs, C. R. Acad. Sci. Paris Sér. I Math. 337 (2003), p. 93-98.
35. p-spaces and applications, in preparation.
36. _, Noncommutative maximal ergodic theorems, J. Amer. Math. Soc. to appear.
37. p non commutatifs, C. R. Acad. Sci. Paris, Sér. I Math. 334 (2002), p. 773-778.
38. _, Noncommutative Burkholder/Rosenthal inequalities, Ann. Probab. 31 (2003), p. 948-995.
39. R. KADISON - A generalized Schwarz inequality and algebraic invariants for operator algebras, Ann. of Math. 56 (1952), p. 494-503.
40. R. KADISON & J. R. RINGROSE - Fundamentals of the theory of operator algebras, I and II, Graduate Studies in Math., Amer. Math. Soc., 1997, 15 and 16.
41. ∞ calculus and sums of closed operators, Math. Ann. 321 (2001), p. 319-345.
42. p-spaces, J. Funct. Anal. 56 (1984), p. 29-78.
43. ∞-functional calculus, in Functional analytic methods for evolution equations (M. Iannelli, R. Nagel & S. Piazzera, eds.), Lect. Notes in Math., vol. 1855, Springer-Verlag, 2004, p. 65-311.
44. F. LANCIEN, G. LANCIEN & C. LE MERDY - A joint functional calculus for sectorial operators with commuting resolvents, Proc. London Math. Soc. 77 (1998), p. 387-414.
45. C. LE MERDY - The similarity problem for bounded analytic semigroups on Hilbert space, Semigroup Forum 56 (1998), p. 205-224.
46. ∞ functional calculus and applications to maximal regularity, Pub. Math. UFR Sci. Tech. Besançon 16 (1999), p. 41-77.
47. ∞ functional calculus on analytic UMD banach spaces, J. Austr. Math. Soc. 74 (2003), p. 351-378.
48. _, The Weiss conjecture for bounded analytic semigroups, J. London Math. Soc. 67 (2003), p. 715-738.
49. _, On square functions associated to sectorial operators, Bull. Soc. Math. France 132 (2004), p. 137-156.
50. J. LINDENSTRAUSS & L. TZAFRIRI - Classical Banach spaces II, Springer-Verlag, 1979.
51. p, C. R. Acad. Sci. Paris 303 (1986), p. 289-292.
52. F. LUST-PIQUARD & G. PISIER - Non-commutative Khintchine and Paley inequalities, Arkiv för Math. 29 (1991), p. 241-260.
53. ∞ functional calculus, in Miniconference on operator theory and partial differential equations, Proc. Centre Math. Appl. Austral. Nat. Univ., vol. 14, Austral. Nat. Univ., 1986, p. 210-231.
54. ∞ functional calculus, in Miniconference on operators in analysis, Proc. Centre Math. Appl. Austral. Nat. Univ., vol. 24, Austral. Nat. Univ., 1989, p. 159-172.
55. T. MEI - Operator valued Hardy spaces, Mem. Amer. Math. Soc., to appear.
56. R. NAGEL - One parameter semigroups of positive operators, Lect. Notes in Math., vol. 1184, Springer-Verlag, 1986.
57. K. R. PARTHASARATHY - An Introduction to Quantum Stochastic Calculus, Monographs in Math., vol. 85, Birkhäuser Verlag, 1992.
58. V. I. PAULSEN - Completely bounded maps and operator algebras, Cambridge Studies in Adv. Math., vol. 78, Cambridge University Press, 2002.
59. G. PISIER - Holomorphic semigroups and the geometry of Banach spaces, Ann. of Math. 115 (1982), p. 375-392.
60. _, Factorization of linear operators and geometry of Banach spaces, CBMS Regional Conf. Series in Math., vol. 60, Amer. Math. Soc., 1986.
61. _, Complex interpolation and regular operators between Banach lattices, Arch. Math. 62 (1994), p. 261-269.
62. p-spaces and completely p-summing maps, Astérisque, vol. 247, Soc. Math. France, 1998.
63. _, Introduction to operator space theory, London Math. Soc. Lect. Note Series, vol. 294, Cambridge University press, 2003.
64. G. PISIER & Q. XU - Non-commutative martingale inequalities, Commun. Math. Phys. 189 (1997), p. 667-698.
65. p-spaces, in Handbook of the geometry of Banach spaces, Vol. II (W. Johnson & J. Lindenstrauss, eds.), Elsevier, 2003, p. 1459-1517.
66. R. J. PLYMEN & P. L. ROBINSON - Spinors in Hilbert space, Cambridge Tracts in Math., vol. 114, Cambridge University Press, 1994.
67. J. PRÜSS - Evolutionary integral equations and applications, Monographs in Math., vol. 87, Birkhäuser Verlag, 1993.
68. N. RANDRIANANTOANINA - Non-commutative martingale transforms, J. Funct. Anal. 194 (2002), p. 181-212.
69. S. SAKAI - C*-algebras and W*-algebras, Classics in Mathematics. Springer-Verlag, 1998.
70. E. M. STEIN - Topics in harmonic analysis related to the Littlewood-Paley theory., Ann. Math. Studies, Princeton University Press, 1970.
71. B. SZ-NAGY & C. FOIAŞ - Harmonic analysis of operators on Hilbert space, Akademiai Kiadó, 1970.
72. M. TAKESAKI - Conditional expectations in von Neumann algebras, J. Functional Analysis 9 (1972), p. 306-321.
73. p-spaces associated with von Neumann algeras, 1981, Notes, Math. Instititue, Copenhagen University.
74. M. UIJTERDIJK - Functional calculi for closed sectorial operators, Ph.D. Thesis, Delft, 1988.
75. D. VOICULESCU - Symmetries of some reduced free product C*-algebras, in Operator algebras and their connections with topology and ergodic theory (Buşteni, 1983), Lect. Notes in Math., vol. 1132, Springer-Verlag, 1985, p. 556-588.
76. D. VOICULESCU, K. DYKEMA & A. NICA - Free random variables, CRM Monograph Series, vol. 1, Amer. Math. Soc., 1992.
77. J. VOIGT - Abstract Stein interpolation, Math. Nachr. 157 (1992), p. 197-199.
78. p- regularity, in Evolution equations and their applications in physical and life sciences (Bad Herrenalb, 1998) (G. Lumer & L. Weis, eds.), Lect. Notes in Pure Appl. Math., vol. 215, Marcel Dekker, 2001, p. 195-214.
79. p-regularity. Math. Ann. 319 (2001), p. 735-758.
80. Q. XU - Recent developments on non-commutative martingale inequalities, in Functional space theory and its applications, Proc. of International Conference and 13th academic symposium in China, Research information Ltd, 2003, p. 283-313.