The little Grothendieck theorem and Khintchine inequalities for symmetric spaces of measurable operators

Journal of Functional Analysis

Volumn 244, Issue 2, 2007, Pages 488-503

  Lust Piquard, Françoise ^a   Xu, Quanhua ^b  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

^b UNIVERSITÉ DE FRANCHE COMTÉ   (France)

Author keywords

Khintchine inequalities; Little Grothendieck theorem; Noncommutative symmetric spaces; Schur multipliers

Indexed keywords

EID: 33846838753     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2006.09.003     Document Type: Article

References (24)

1. Dodds P., Dodds T., and de Pagter B. Noncommutative Köthe duality. Trans. Amer. Math. Soc. 339 (1993) 717-750
2. Fack Th., and Kosaki H. Generalized s-numbers of τ-measurable operators. Pacific J. Math. 123 (1986) 269-300
3. *-algebras. Adv. Math. 56 (1985) 93-116
4. Lindenstrauss J., and Tzafriri L. Classical Banach Spaces. II (1979), Springer-Verlag, Berlin
5. p (1 < p < ∞). C. R. Acad. Sci. Paris Sér. I Math. 303 (1986) 289-292
6. Lust-Piquard F. A Grothendieck factorization theorem on 2-convex Schatten spaces. Israel J. Math. 79 (1992) 331-365
7. Lust-Piquard F. On the coefficient problem: A version of the Kahane-Katznelson-De Leeuw theorem for spaces of matrices. J. Funct. Anal. 149 (1997) 352-376
8. Lust-Piquard F., and Pisier G. Noncommutative Khintchine and Paley inequalities. Ark. Mat. 29 (1991) 241-260
9. p. Astérisque 11 (1974)
10. Ovčinnikov V.I. Symmetric spaces of measurable operators. Dokl. Akad. Nauk SSSR 191 (1970) 769-771
11. Pelczynski A., and Sukochev F. Some remarks on Toeplitz multiplers and Hankel matrices. Studia Math. 175 (2006) 175-204
12. *-algebras, with an appendix on Grothendieck's constants. J. Funct. Anal. 29 (1978) 397-415
13. Pisier G. Some applications of the complex interpolation method to Banach lattices. J. Anal. Math. 35 (1979) 264-281
14. p 1 and noncommutative generalizations. Math. Ann. 276 (1986) 105-136
15. Pisier G. Factorization of Linear Operators and Geometry of Banach Spaces. CBMS Reg. Conf. Ser. Math. vol. 60 (1986), Washington, DC
16. Pisier G. The Volume of Convex Bodies and Banach Space Geometry. Cambridge Tracts in Math. vol. 94 (1989), Cambridge Univ. Press, Cambridge
17. Pisier G., and Shlyakhtenko D. Grothendieck's theorem for operator spaces. Invent. Math. 150 (2002) 185-217
18. p-spaces. Handbook of the Geometry of Banach Spaces vol. 2 (2003), North-Holland, Amsterdam 1459-1517
19. Takesaki M. Theory of Operator Algebras. I (1979), Springer-Verlag, New York
20. Tomczak-Jaegermann N. Uniform convexity of unitary ideals. Israel J. Math. 48 (1984) 249-254
21. Xu Q. Convexité uniforme des espaces symétriques d'opérateurs mesurables. C. R. Acad. Sci. Paris Sér. I Math. 309 (1989) 251-254
22. Xu Q. Analytic functions with values in lattices and symmetric spaces of measurable operators. Math. Proc. Cambridge Philos. Soc. 109 (1991) 541-563
23. Xu Q. Radon-Nikodým property in symmetric spaces of measurable operators. Proc. Amer. Math. Soc. 115 (1992) 329-335
24. p-spaces. Duke Math. J. 131 (2005) 525-574