Projective Hilbert modules and sequential approximations

作     者：Lawrence G.Brown Huaxin Lin 

作者机构：Department of Mathematics Purdue University Department of Mathematics East China Normal University Department of Mathematics University of Oregon 

出 版 物：《Science China Mathematics》 (中国科学:数学(英文版))

年 卷 期：2024年

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Science Foundation of the US (Grant No. DMS1954600) partially funded by the Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Science and Technology Commission of Shanghai Municipality (Grant Nos. 13dz2260400 and 22DZ2229014) 

摘      要：We show that when A is a separable C*-algebra, every countably generated Hilbert A-module is projective(with bounded module maps as morphisms). We also study the approximate extensions of bounded module maps. In the case where A is a σ-unital simple C*-algebra with strict comparison, and every strictly positive lower semicontinuous affine function on quasitraces can be realized as the rank of an element in the Cuntz semigroup, we show that the Cuntz semigroup is equivalent to unitarily equivalent classes of countably generated Hilbert A-modules if and only if A has stable rank one.