Continuity of functors with respect to generalized inductive limits |
| |
Authors: | Jiajie HUA Xiaochun FANG Xiao-Ming XU |
| |
Institution: | 1. School of Mathematics Physics and Information Engineering, Jiaxing University, Jiaxing 314001, China2. Department of Mathematics, Tongji University, Shanghai 200092, China3. School of Science, Shanghai Institute of Technology, Shanghai 201418, China |
| |
Abstract: | Let be a generalized inductive system of a sequence (Ai) of unital separable C*-algebras, with . Set for all i>j: We prove that if are order zero completely positive contractions for all j and i>j; and for all j and i>j}>0; where is the spectrum of ; then ; where Cu(A) is a stable version of the Cuntz semigroup of C*-algebra A: Let be a generalized inductive system of C*-algebras, with the order zero completely positive contractions. We also prove that if the decomposition rank (nuclear dimension) of An is no more than some integer k for each n; then the decomposition rank (nuclear dimension) of A is also no more than k: |
| |
Keywords: | Completely positive map order zero generalized inductive limits classification of C*-algebra |
本文献已被 维普 等数据库收录! |
| 点击此处可从《Frontiers of Mathematics in China》浏览原始摘要信息 |
| 点击此处可从《Frontiers of Mathematics in China》下载免费的PDF全文 |