关于强奇异极大交换子代数(英文)  

On Strongly Singular Maximal Abelian Subalgebras

作　　者：王利广[1] 温玉珍[1] 

机构地区：[1]曲阜师范大学数学系

出　　处：《数学进展》2005年第4期488-496,共9页Advances in Mathematics（China）

基　　金：The work was supported by National Natural Science Foundation of China(No. 10301004)

摘　　要：设M_1和M_2是有限的冯·诺依曼代数,τ_1和τ_2是M_1和M_2的正规的,忠实的,正规化的迹.假设A_1和A_2分别是M_1和M_2的极大交换子代数,E_(Ai)是由M_i到A_i 的保迹的条件期望(i=1,2).若E_(A1)和E_(A2)是渐近同态条件期望,则A_1■A_2是M_1■M_2的强奇异极大交换子代数.另外,我们证明了若A是没有原子的有限冯·诺依曼代数M_1的强奇异极大交换子代数,M_2是有限冯·诺依曼代数,则A是M_1和M_2的约化自由积M_1*M_2 的强奇异极大交换子代数.Let M1 and M2 be finite von Neumann algebras with normal faithful normalized traces τl and τ2 respectively. Suppose A1 and A2 are maximal abelian subalgebras of M1 and M2 respectively. Let EAi be the trace preserving conditional expectation of Mi onto Ai （i = 1, 2）. If EA1 and EA2 are asymptotic homomorphisms, then A1 A2 is a strongly singular maximal abelian subalgebra of M1 M2. We also show that if A is a strongly singular maximal abelian subalgebra of a non-atomic finite von Neumann algebra M1 and M2 is a finite von Neumann algebra, then A is also a strongly singular maximal abelian subalgebra of M1 ＊ M2, the reduced free product of M1 and M2.

关 键 词：渐近同态 约化自由积 强奇异极大交换子代数 张量积 冯·诺依曼代数 

分 类 号：O177.5[理学—数学]