Geodesic
Characterization of subdiagonal algebras on noncommutative Lorentz spaces
Eurasian mathematical journal, Tome 6 (2015) no. 3, pp. 6-12.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $(\mathcal{M}, \tau)$ be a finite von Neumann algebra, $\mathcal{A}$ be a tracial subalgebra of $\mathcal{M}$. We prove that $\mathcal{A}$ has $L^{p,q}$-factorization if and only if $\mathcal{A}$ is a subdiagonal algebra. We also obtain some characterizations of subdiagonal algebras. 
@article{EMJ_2015_6_3_a0,
     author = {T. N. Bekjan and A. Kairat},
     title = {Characterization of subdiagonal algebras on noncommutative {Lorentz} spaces},
     journal = {Eurasian mathematical journal},
     pages = {6--12},
     publisher = {mathdoc},
     volume = {6},
     number = {3},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2015_6_3_a0/}
}
TY  - JOUR
AU  - T. N. Bekjan
AU  - A. Kairat
TI  - Characterization of subdiagonal algebras on noncommutative Lorentz spaces
JO  - Eurasian mathematical journal
PY  - 2015
SP  - 6
EP  - 12
VL  - 6
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2015_6_3_a0/
LA  - en
ID  - EMJ_2015_6_3_a0
ER  - 
%0 Journal Article
%A T. N. Bekjan
%A A. Kairat
%T Characterization of subdiagonal algebras on noncommutative Lorentz spaces
%J Eurasian mathematical journal
%D 2015
%P 6-12
%V 6
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2015_6_3_a0/
%G en
%F EMJ_2015_6_3_a0
T. N. Bekjan; A. Kairat. Characterization of subdiagonal algebras on noncommutative Lorentz spaces. Eurasian mathematical journal, Tome 6 (2015) no. 3, pp. 6-12. http://geodesic.mathdoc.fr/item/EMJ_2015_6_3_a0/

[1] W. B. Arveson, “Analyticity in operator algebras”, Amer. J. Math., 89 (1967), 578–642 | DOI | MR | Zbl

[2] T. N. Bekjan, “Characterization of subdiagonal algebras”, Proc. Amer. Math. Soc., 139 (2011), 1121–1126 | DOI | MR | Zbl

[3] D. P. Blecher, L. E. Labuschagne, “Applications of the Fuglede–Kadison determinant: Szegö's theorem and outers for noncommutative $H^p$”, Trans. Am. Math. Soc., 360 (2008), 6131–6147 | DOI | MR | Zbl

[4] D. P. Blecher, L. E. Labuschagne, “Characterizations of noncommutative $H^\infty$”, Integr. Equ. Oper. Theory, 56 (2006), 301–321 | DOI | MR | Zbl

[5] M. Cwikel, Y. Sagher, “$(L(p,\infty))$”, Indiana Univ. Math. J., 21 (1972), 781–786 | DOI | MR | Zbl

[6] V. Chilin, S. Litvinov, A. Skalski, “A fewremarks in non-commutative ergodic theory”, J. Operator Theory, 53 (2005), 331–350 | MR | Zbl

[7] T. Fack, H. Kosaki, “Generalized $s$-numbers of $\tau$-measure operators”, Pac. J. Math., 123 (1986), 269–300 | DOI | MR | Zbl

[8] L. Grafakos, Classical and modern Fourier analysis, Pearson Education, London, 2004 | MR | Zbl

[9] R. A. Hunt, “On $L(p,q)$ spaces”, L' Enseignement Math., 12 (1966), 249–276 | MR | Zbl

[10] Y. Han, T. N. Bekjan, “The dual of noncommutative Lorentz spaces”, Acta. Math. Sci., 31 (2011), 2067–2080 | DOI | MR | Zbl

[11] M. Marsalli, G. West, “Noncommutative $H^p$-spaces”, J. Operator Theory, 40 (1997), 339–355 | MR

[12] E. Nelson, “Notes on non-commutative integration”, J. Funct. Anal., 15 (1974), 103–116 | DOI | MR | Zbl

[13] G. Pisier, Q. Xu, “Noncommutative $L_P$-spaces”, Handbook of the geometry of Banach spaces, v. 2, North-Holland, Amsterdam, 2003, 1459–1517 | DOI | MR | Zbl

[14] J. Shao, Y. Han, “Szegö type factorization theorem for noncommutative Hardy–Lorentz spaces”, Acta Math. Sci., 33:6 (2013), 1675–1684 | DOI | MR | Zbl

[15] Q. Xu, “Interpolation of operator spaces”, J. Funct. Anal., 139 (1996), 500–539 | DOI | MR | Zbl