Turdebek N. BEKJAN , Kordan N. OSPANOV . COMPLEX INTERPOLATION OF NONCOMMUTATIVE HARDY SPACES ASSOCIATED WITH SEMIFINITE VON NEUMANN ALGEBRAS[J]. Acta mathematica scientia, Series B, 2020 , 40(1) : 245 -260 . DOI: 10.1007/s10473-020-0117-9

[1] Arveson W B. Analyticity in operator algebras. Amer J Math, 1967, 89:578-642
[2] Bekjan T N. Noncommutative Hardy space associated with semifinite subdiagonal algebras. J Math Anal Appl, 2015, 429:1347-1369
[3] Bekjan T N, Xu Q. Riesz and Szegö type factorizations for noncommutative Hardy spaces. J Operator Theory, 2009, 62:215-231
[4] Bekjan T N, Chen Z, Liu P, Jiao Y. Noncommutative weak Orlicz spaces and martingale inequalities. Studia Math, 2011, 204(3):195-212
[5] Bergh J, Lófstróm J. Interpolation Spaces, an Introduction. Berlin, Heidelberg, New York:Springer-Verlag, 1976
[6] Bergh J. On the relation between the two complex methods of interpolation. Indiana Univ Math J, 1979, 28:775-778
[7] Bennett C, Sharpley R. Interpolation of Operators. London:Academic Press, 1988
[8] Blecher D P, Labuschagne L E. Characterization of noncommutaive H^∞. Integr Equ Oper Theory, 2006, 56:301-321
[9] Blecher D P, Labuschagne L E. Applications of the Fuglede-Kadison determinant:Szegö's theorem and outers for noncommutatuve H^p. Trans Amer Math Soc, 2008, 360:6131-6147
[10] Blecher D P, Labuschagne L E. A Beurling theorem for noncommutative L^p. J Operator Theory, 2008, 59:29-51
[11] Blecher D P, Labuschagne L E. Von Neumann algebraic H^p theory//Proceedings of the Fifth Conference on Function Spaces. Contemporary Mathematics 435. Amer Math Soc, 2007:89-114
[12] Calderón A P. Intermediate spaces and interpolation, the complex method. Studia Math, 1964, 24:133-190
[13] Cwikel M, Janson S. Interpolation of analytic families of operators. Studia Math, 1984, 79(1):61-71
[14] Dodds P G, Dodds T K, de Pager B. Noncommutative Banach function spaces. Math Z, 1989, 201:583-587
[15] Dodds P G, Dodds T K, de Pager B. Fully symmetric operator spaces. Integr Equ Oper Theory, 1992, 15:942-972
[16] Exel R. Maximal subdiagonal algebras. Amer J Math, 1988, 110:775-782
[17] Fack T, Kosaki H. Generalized s-numbers of τ-measurable operators. Pac J Math, 1986, 123:269-300
[18] Janson S. Interpolation of subcouples and quotient couples. Ark Mat, 1993, 31:307-338
[19] Ji G. Maximality of semifinite subdiagonal algebras. Journal of Shaanxi Normal University (Natural Science Edition), 2000, 28(1):15-17
[20] Jones P. L^∞ estimates for the ∂-problem in a half plane. Acta Math, 1983, 150:137-152
[21] Junge M. Doob's inequality for noncommutative martingales. J Reine Angew Math, 2002, 549:149-190
[22] Kisliakov S. Interpolation of H^p-spaces:some recent developments//Function Spaces, Interpolation Spaces, and Related Topics (Haifa 1995). Israel Mathematica and Conference Proceedings, Bar-Ilan University, Ramat Gan, 1999, 13:102-140
[23] Labuschagne L E. Analogues of composition operators on non-commutative H^p spaces. J Operator Theory, 2003, 49:115-141
[24] Marsalli M. Noncommutative H² spaces. Proc Amer Math Soc, 1997, 125:779-784
[25] Marsalli M, West G. Noncommutative H^p-spaces. J Operator Theory, 1997, 40:339-355
[26] Marsalli M, West G. The dual of noncommutative H¹. Indiana Univ Math J, 1998,47:489-500
[27] Pisier G. Interpolation between H^p spaces and non-commutative generalizations I. Pacific J Math, 1992, 155:341-368
[28] Pisier G, Xu Q. Non-commutative L^p-spaces//Handbook of the Geometry of Banach Spaces 2. Amsterdam:North-Holland, 2003:1459-1517
[29] Randrianantoanina N. Hilbert transform associated with finite maximal subdiagonal algebras. Austral Math Soc (Series A), 1999, 65:388-404.
[30] Sakai S. C^*-algebras and W^*-algebras. New York:Springer-Verlag, 1971
[31] Saito K-S. A note on invariant subspaces for finite maximal subdiagonal algebras. Proc Amer Math Soc, 1979, 77:348-352
[32] Shao J, Han Y. Szego type factorization theorem for noncommutative Hardy-Lorentz space. Acta Math Sci, 2013, 33B(6):1675-1684
[33] Sukochev F, Tulenov K, Zanin D. Nehari-type theorem for non-commutative Hardy spaces. J Geom Anal, 2017, 27(3):1789-1802
[34] Wolff T. A note on interpolation spaces. Springer Lecture Notes in Math, 1982, 908:199-204
[35] Xu Q. Analytic functions with values in lattices and symmetric spaces of measurable operators. Math Proc Camb Phil Soc, 1991, 109:541-563
[36] Xu Q. Applications du théorème de factorisation pour des à fonctions o valeurs in lattices opératours. Studia Math, 1990, 95:273-292
[37] Xu Q. Non-commutative L^p-spaces. preprint