On maximal non-selfadjoint reflexive algebras associated with a double triangle lattice  

作　　者：DONG AiJu WANG Dong 

机构地区：[1]School of Mathematics and Computer Engineering,Xi'an University of Arts and Science [2]Academy of Mathematics and Systems Science,Chinese Academy of Sciences [3]Department of Mathematics and Statistics,University of New Hampshire

出　　处：《Science China Mathematics》2015年第11期2373-2386,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11371290)

摘　　要：We show that the reflexive algebra Alg(L) given by a double triangle lattice L in a finite factor M(with L" = M) is maximal non-selfadjoint in the class of all weak operator closed subalgebras with the same diagonal subalgebra Alg(L) ∩ Alg(L)^+.Our method can be used to prove similar results in finite-dimensional matrix algebras.As a consequence,we give a new proof to the main theorem by Hou and Zhang(2012).We show that the reflexive algebra Alg（L） given by a double triangle lattice L in a finite factor M （with L＂ = M） is maximal non-selfadjoint in the class of all weak operator closed subalgebras with the same diagonal subalgebra Alg（L） ∩ Alg（L）＊. Our method can be used to prove similar results in finite-dimensional matrix algebras. As a consequence, we give a new proof to the main theorem by Hou and Zhang （2012）.

关 键 词：Kadison-Singer algebra Kadison-Singer lattice reflexive algebra double triangle lattice factorof type II1 

分 类 号：O153[理学—数学]