标准C*代数间保持一类正元比较关系的映射

Mapping on Standard C*algebras Preserving Comparison for Positive Elements

摘要:

假设H是一个复Hilbert空间,AH是H上的一个标准C*代数,AH+是AH中所有正元构成的集合.1977年,Cuntz引入了C*代数中正元的比较关系.设A是一个C*代数,任给A,B∈A+,若存在X∈A+,使得A=XBX*,则记A≤B.文章刻画了定义在AH+上的所有双边保持此关系的弱连续半线性满射.

Abstract:

Let H be a complex Hilbert space,AH the standard C*algebra on H,and AH+ the set of all positive elements in AH.In 1977,Cuntz introduced a comparison in the set of all positive elements in a C*algebra.Let A be a C*algebra.For A,B∈A+,we write A≤B if there exists an element X∈A such that A=XBX*.In this paper,we characterize all weakly continuous semilinear surjective maps on AH+ which preserves the positive elements comparison in both directions.