Acta mathematica scientia, Series B >
SZEGÖ|TYPE FACTORIZATION THEOREM FOR NONCOMMUTATIVE HARDY-LORENTZ SPACES
Received date: 2012-05-03
Revised date: 2013-06-01
Online published: 2013-11-20
Supported by
Partially supported by NSFC (11071204) and XJUBSCX-2012002.
We introduce noncommutative Hardy-Lorentz spaces and give the Szeg¨o and inner-outer type factorizations of these spaces.
SHAO Jing-Jing , HAN Ya-Zhou . SZEGÖ|TYPE FACTORIZATION THEOREM FOR NONCOMMUTATIVE HARDY-LORENTZ SPACES[J]. Acta mathematica scientia, Series B, 2013 , 33(6) : 1675 -1684 . DOI: 10.1016/S0252-9602(13)60114-9
[1] Arveson W B. Analyticity in operator algebras. Amer J Math, 1967, 89: 578–642
[2] Blecher D P, Labuschagne L E. Applications of the Fuglede-Kadison determinant: Szeg¨o theorem and outers for noncommutative Hp. Trans Amer Math Soc, 2008, 360: 6131–6147
[3] Brown L G. Lidskii’s theorem in the type II case//Geometric Methods in Operator Algebras (Kyoto 1983). Pitman Res Notes Math Ser, Vol 123. Harlow: Longmam Sci Tech, 1986: 1–35
[4] Bekjan N, Xu Q. Riesz and Szeg¨o type factorizations for noncommutative Hardy spaces. J Oper Theory, 2009, 62(1): 215–231
[5] Fack T, Kosaki H. Generalized s-numbers of τ-measurable operators. Pacific J Math 1986, 123: 269–300
[6] Fuglede B, Kadison R V. Determinant theory in finite factors. Ann Math, 1952, 55: 520–530
[7] Hunt R A. On L(p, q) spaces. L’Enseignement Math, 1966, 12: 249–276
[8] Han Yazhou, Bekjan T N. The dual of noncommutataive Lorentz spaces. Acta Math Sci, 2011, 31B(6): 2067–2080
[9] Helson H, Lowdenslager D. Prediction theory and Fourier series in several variables. I. Acta Math, 1958, 99: 165–202
[10] Haagerup U, Schultz H. Brown measures of unbounded operators affiliated with a finite von Neumann algebra. Math Scand, 2007, 100: 209–263
[11] Labuschagne L E. A noncommutative Szeg¨o theorem for subdiagonal subalgebras of von Neumann algebras.
Proc Amer Math Soc, 2005, 133: 3643–3646
[12] Marsalli M, West G. Noncommutative Hp spaces. J Oper Theory, 1998, 40: 339–355
[13] Masani P, Wiener N. The prediction theory of multivariate stochastic processes. Acta Math, 1957, 98: 111–150
[14] Masani P, Wiener N. The prediction theory of multivariate stochastic processes. II. Acta Math, 1958, 99: 93–137
[15] Pisier G, Xu Q. Non-commutative Lp-spaces//Handbook of the Geometry of Banach Spaces, Vol 2. Amsterdam:
North-Holland, 2003: 1459–1517
[16] Szeg¨o G. Beitr¨age zur theorie der Toeplitzschen formen. I. Math Z, 1920, 6: 167–202
[17] Srinivasan T, Wang J K. Weak-Dirchlet algebras//Proceedings of the International Symposium on Function
Algebras. Tulane University, 1965(Chicago). Scott-Foresman, 1966: 216–249
[18] Xu Q. Noncommutative Lp-spaces. Preprint
[19] Xu Q. Interpolation of operator spaces. J Funct Anal, 1996, 139: 500–539
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