非自伴算子代数间的等距代数同构  

Isometrically Algebraic Isomorphisms between Two Non-self-adjoint Operator Algebras

作　　者：纪培胜[1] 

机构地区：[1]中国科学院数学研究所

出　　处：《数学学报（中文版）》1996年第4期477-482,共6页Acta Mathematica Sinica：Chinese Series

摘　　要：设Ｇｉ是满足第二可数性公理的、Ｈａｕｓｄｏｒｆｆ的、顺从的、ｒ－离散的、主的局部紧群胚，并且有一个紧开Ｇ－集覆盖；设Ｐｉ是Ｇｉ中含Ｇ＿ｉ￣０的开闭集，且满足及相应的模是具有性质ＤＣ的Ｃ（Ｇｉ）的子代数（ｉ＝１，２）．本文证明从Ａ（Ｐ１）到Ａ（Ｐ２）上的每一个等距代数同构可以扩张成从Ｃ（Ｇ１）到Ｃ（Ｇ２）上的Ｃ－同构，进一步，可以对Ｃ（Ｇ２）重新坐标化，使得这个Ｃ－同构可由一个群胚同构生成．It is shown that if Pi is a clopen subset of Gi containing with Pi Pi-1=Gi inthe amenable, r-discrete, principal local compact groupoid Gi which has a cover of compact openG-sets, and A(Pi) is a subalgebra with property DC of C*(Gi) (i=1, 2), then every isometricallyalgebraic isomorphism from A(P1) onto A(P2) can be extended to a C*-isomorphism from C* (G1)onto C*(G2). Moreover, we can coordinate C*(G2) to be C*(G'2) such that this C*-isomorphismcan be implemented by a groupoid isomorphism from G1 onto G'2.

关 键 词：群胚 等距代数同构 非自伴算子代数 C^＊代数 

分 类 号：O177.5[理学—数学]