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.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
1996年第4期477-482,共6页
Acta Mathematica Sinica：Chinese Series
