Fourier analysis, Schur multipliers on $S^p$ and non-commutative Λ(p)-sets

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1. [1] M. Anoussis and E. Katsoulis, Complemented subspaces of $C^p$ spaces and CSL algebras, J. London Math. Soc. 45 (1992), 301-313. Zbl0781.47037
2. [2] J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, New York, 1976. Zbl0344.46071
3. [3] G. Bennett, Some ideals of operators on Hilbert space, Studia Math. 55 (1976), 27-40. Zbl0338.47013
4. [4] D. Blecher and V. Paulsen, Tensor products of operator spaces, J. Funct. Anal. 99 (1991), 262-292. Zbl0786.46056
5. [5] A. Bonami, Ensembles Λ(p) dans le dual de $D^{\infty }$, Ann. Inst. Fourier (Grenoble) 18 (1968), no. 2, 193-204. 
6. [6] A. Bonami, Étude des coefficients de Fourier des fonctions de $L^p\left(G\right)$, ibid. 20 (1970), no. 2, 335-402. Zbl0195.42501
7. [7] J. Bourgain, Some remarks on Banach spaces in which martingale differences are unconditional, Ark. Mat. 21 (1983), 163-168. Zbl0533.46008
8. [8] J. Bourgain, Vector valued singular integrals and the $H^1$-BMO duality, in: Probability Theory and Harmonic Analysis, J. A. Chao and W. Woyczynski (eds.), Marcel Dekker, New York, 1986, 1-19. 
9. [9] J. Bourgain, Bounded orthogonal systems and the Λ(p)-set problem, Acta Math. 162 (1989), 227-245. Zbl0674.43004
10. [10] M. Bożejko, The existence of Λ(p) sets in discrete noncommutative groups, Boll. Un. Mat. Ital. (4) 8 (1973), 579-582. Zbl0279.43010
11. [11] M. Bożejko, A remark to my paper (The existence of Λ(p) sets in discrete noncommutative groups), ibid. 11 (1975), 198-199. Zbl0304.43009
12. [12] M. Bożejko, On Λ(p) sets with minimal constant in discrete noncommutative groups, Proc. Amer. Math. Soc. (2) 51 (1975), 407-412. 
13. [13] M. Bożejko, Remarks on the Herz-Schur multipliers on free groups, Math. Ann. 258 (1981), 11-15. Zbl0483.43004
14. [14] M. Bożejko and G. Fendler, Herz-Schur multipliers and completely bounded multipliers of the Fourier algebra of a locally compact group, Boll. Un. Mat. Ital. A (6) 3 (1984), 297-302. Zbl0564.43004
15. [15] J. Diestel, H. Jarchow and A. Tonge, Absolutely Summing Operators, Cambridge Univ. Press, 1995. Zbl0855.47016
16. [16] J. Dixmier, Formes linéaires sur un anneau d'opérateurs, Bull. Soc. Math. France 81 (1953), 9-39. Zbl0050.11501
17. [17] E. Effros and Z. Ruan, A new apprach to operator spaces, Canad. Math. Bull. 34 (1991), 329-337. Zbl0769.46037
18. [18] J. Erdos, Completely distributive CSL algebras with no complements in $S^p$, Proc. Amer. Math. Soc. 124 (1996), 1127-1131. Zbl0856.47027
19. [19] U. Haagerup and G. Pisier, Bounded linear operators between $C^{*}$-algebras, Duke Math. J. 71 (1993), 889-925. Zbl0803.46064
20. [20] H. Kosaki, Applications of the complex interpolation method to a von Neumann algebra: Non-commutative $L^p$-spaces, J. Funct. Anal. 56 (1984), 29-78. Zbl0604.46063
21. [21] S. Kwapień, On operators factorizable through $L_p$ space, Bull. Soc. Math. France Mém. 31-32 (1972), 215-225. Zbl0246.47040
22. [22] S. Kwapień and A. Pełczyński, The main triangle projection in matrix spaces and its applications, Studia Math. 34 (1970), 43-68. Zbl0189.43505
23. [23] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, Vol. I, Sequence Spaces, Springer, Berlin, 1976. Zbl0347.46025
24. [24] J. López and K. Ross, Sidon Sets, Lecture Notes in Pure and Appl. Math. 13, Marcel Dekker, New York, 1975. 
25. [25] F. Lust-Piquard, Opérateurs de Hankel 1-sommant de l(N) dans l(N) et multiplicateurs de $H^1\left(T\right)$, C. R. Acad. Sci. Paris Sér. I 299 (1984), 915-918. Zbl0562.42007
26. [26] F. Lust-Piquard, Inégalités de Khintchine dans $C_p$ (1 < p < ∞), ibid. 303 (1986), 289-292. 
27. [27] F. Lust-Piquard and G. Pisier, Non-commutative Khintchine and Paley inequalities, Ark. Mat. 29 (1991), 241-260. Zbl0755.47029
28. [28] E. Nelson, Notes on non-commutative integration, J. Funct. Anal. 15 (1974), 103-116. Zbl0292.46030
29. [29] V. Peller, Hankel operators of class ${ɞ}_p$ and their applications (rational approximation, Gaussian processes, the problem of majorization of operators), Mat. Sb. 113 (1980), 538-551 (in Russian); English transl.: Math. USSR-Sb. 41 (1982), 443-479. Zbl0458.47022
30. [30] V. Peller, Vectorial Hankel operators, commutators and related operators of the Schatten-von Neumann class ${ɞ}_p$, Integral Equations Operator Theory 5 (1982), 244-272. Zbl0478.47014
31. [31] G. Pisier, Some results on Banach spaces without local unconditional structure, Compositio Math. 37 (1978), 3-19. Zbl0381.46010
32. [32] G. Pisier, Similarity Problems and Completely Bounded Maps, Lecture Notes in Math. 1618, Springer, 1995. 
33. [33] G. Pisier, The operator Hilbert space OH, complex interpolation and tensor norms, Mem. Amer. Math. Soc. 585 (1996). Zbl0932.46046
34. [34] G. Pisier, Non-commutative vector valued $L_p$-spaces and completely p-summing maps, Astérisque 247 (1998). 
35. [35] G. Pisier and Q. Xu, Non-commutative martingale inequalities, Comm. Math. Phys. 189 (1997), 667-698. Zbl0898.46056
36. [36] Z. Ruan, Subspaces of $C^{*}$-algebras, J. Funct. Anal. 76 (1988), 217-230. 
37. [37] W. Rudin, Trigonometric series with gaps, J. Math. Mech. 9 (1960), 203-228. Zbl0091.05802
38. [38] I. Segal, A non-commutative extension of abstract integration, Ann. of Math. 37 (1953), 401-457. Zbl0051.34201
39. [39] J. Stafney, The spectrum of an operator on an interpolation space, Trans. Amer. Math. Soc. 144 (1969), 333-349. Zbl0225.46034
40. [40] J. Stafney, Analytic interpolation of certain multiplier spaces, Pacific J. Math. 32 (1970), 241-248. Zbl0187.37702
41. [41] E. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, NJ, 1971. Zbl0232.42007
42. [42] M. Talagrand, Sections of smooth convex bodies via majorizing measures, Acta Math. 175 (1995), 273-306. Zbl0917.46006
43. [43] N. Tomczak-Jaegermann, The moduli of smoothness and convexity and the Rademacher averages of trace classes $S_p(1\le p<\infty )$, Studia Math. 50 (1974), 163-182. Zbl0282.46016
44. [44] N. Varopoulos, Tensor algebras over discrete spaces, J. Funct. Anal. 3 (1969), 321-335. Zbl0183.14502
45. [45] M. Zafran, Interpolation of multiplier spaces, Amer. J. Math. 105 (1983), 1405-1416. Zbl0544.42010
46. [46] A. Zygmund, On Fourier coefficients and transforms of functions of two variables, Studia Math. 50 (1974), 189-201. Zbl0278.42005