Path connectivity of idempotents on a Hilbert space |
| |
| Authors: | Yan-Ni Chen Hong-Ke Du Hai-Yan Zhang |
| |
| Institution: | Department of Mathematics, Shaanxi University of Technology, Hanzhong 723001, People's Republic of China ; College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, People's Republic of China ; College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, People's Republic of China |
| |
| Abstract: | Let  and  be two idempotents on a Hilbert space. In 2005, J. Giol in Segments of bounded linear idempotents on a Hilbert space, J. Funct. Anal. 229(2005) 405-423] had established that, if  is invertible, then  and  are homotopic with  In this paper, we have given a necessary and sufficient condition that  where  denotes the minimal number of segments required to connect not only from  to  , but also from  to  in the set of idempotents. |
| |
| Keywords: | Idempotent orthogonal projection homotopic path connectivity |
|
| 点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息 |
| 点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文 |
|
