阿布都艾尼·阿布都热西提. 关于非交换Orlicz空间的对角子代数（英文）[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 2014, 31(4): 411-414.DOI：
关于非交换Orlicz空间的对角子代数（英文）
摘要
设Φ是增长函数
M是正规有限忠实迹的von Neumann代数
A是M的一个迹子代数.首先证明了条件期望E的收缩性
其次证明了A有LΦ-分解当且仅当A是对角子代数.另外还给出了对角子代数的一些特征.
Abstract
Let Φ be a growth function
M be finite von Neumann algebra with a faithful normal tracial state τ and A be a tracial subalgebra of M. We proved contractivity of conditional expectation E and A has LΦ-factorization if and only if A is a subdiagonal algebra. We also gave some characterizations of subdiagonal algebras.
关键词
Keywords
references
Arveson W B.Analyticity in operator algebras[J].Amer J Math,1967,89:578-642.
Bekjan T N,Xu Q.Riesz and Szeg¨o type factorizations for noncommutative Hardy spaces[J].J Oper Theory,2009,62(1):215–231.
Abdurexit A,Bekjan T.Noncommutative Orlicz-Hardy spaces associated with growth functions[J].J Math Anal Appl,2014,420:824-834.
Ji G,Saito K S.Factorization in Sundiagonal Algebras[J].J Funct Anal,1998,159:191-202.
Blecher D P,Labuschagne L E.A Beurling theorem for noncommutative Lp spaces[J].J Oper Theory,2008,59:29-51.
Saito K S.A note on invariant subspaces for maximal subdiagonal algebras[J].Proc Amer Math Soc,1979,77:349-352.
Labuschagne L E.A noncommutative Szeg¨o theorem for subdiagonal subalgebras of von Neumann algebras[J].Proc Amer Math Soc,2005,133:3643–3646.
Blecher D P,Labuschagne L E.Applications of the Fuglede-Kadison determinant:Szeg¨o’s theorem and outers for noncommutative Hp[J].Trans Am Math Soc,2008,360:6131-6147.
Bekjan T N.Characterization of subdiagonal algebras[J].Proc Amer Math Soc,2011,139:1121-1126.
京公网安备11010802024621