有关C~*-代数上的投影提升问题  

On Lift of Projections of C~*-Algebras

作　　者：方小春[1] 于静[1] 王琳[1] 

机构地区：[1]同济大学数学系,上海200092

出　　处：《同济大学学报（自然科学版）》2008年第2期277-279,共3页Journal of Tongji University:Natural Science

基　　金：国家自然科学基金资助项目(10771161)

摘　　要：利用投影的对角化,回答了何时C*-代数A的商代数M(A)/A上的投影可以提升为M(A)中的投影这一问题,具体给出了两个等价条件:投影的正元提升是弱拟对角的;投影存在形如∞∑i=1ai的正元提升,其中{ai}是两两正交的正元.对一般的商代数A/I,如果投影p,q存在A中提升p1,q1,且满足σ(p1q1p1)≠[0,1],那么p,q可以提升成保持其直交性及大小关系的投影.The paper answers when the projections of algebra M（ A ）/A can lift to the projection of M（ A ） on the basis of diagonalization of projection in M（A ）, and gives two equivalent conditions： the positive lift of projection is weakly-quasidiagonal; the projection lifts to positive element of the form ∞∑i=1ai, where {ai} are mutually orthogonal positive elements. For general quotient algebra A/I,if projections p, q lift to p1, q1 such that a（p1 q1P1 ）≠[0, 1], then p, q can lift to projections preserving their orthogonality and big and small relations.

关 键 词：C＊代数 投影 对角化 谱 提升 

分 类 号：O177.5[理学—数学]