AFC~*-代数上的映射

MAPS ON AF C~*-ALGEBRAS

本文讨论AFC代数中的一些映射的线性性质和它们的局部性质之间的关系,研究AFC代数A上的保持乘法的局部自同构在A中矩阵单位系上的作用,证明了是A上的自同构。对于UHF代数上满等距的结构,还证明了UHF代数上的2局部(满线性)等距是线性的.

In this paper, we study the relationship between the linear property of some maps on AF C^＊ -algebras and their local property. We prove that every multiplicative local automorphism Ф on an AF C^＊ -algebra A is an automorphism by studying the action of Ф on a matrix system of A. We also prove that every 2-local isomety of UHF algebra is linear by studying the structure of the surjective isometry on UHF algebra.