Path connectivity of idempotents on a Hilbert space
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- by Yan-Ni Chen, Hong-Ke Du and Hai-Yan Zhang PDF
- Proc. Amer. Math. Soc. 136 (2008), 3483-3492 Request permission
Abstract:
Let $P$ and $Q$ 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 $P+Q-I$ is invertible, then $P$ and $Q$ are homotopic with $\tilde {s}(P,Q)\leq 2.$ In this paper, we have given a necessary and sufficient condition that $\tilde {s}(P,Q)\leq 2,$ where $\tilde {s}(P,Q)$ denotes the minimal number of segments required to connect not only from $P$ to $Q$, but also from $Q$ to $P$ in the set of idempotents.References
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Additional Information
- Yan-Ni Chen
- Affiliation: Department of Mathematics, Shaanxi University of Technology, Hanzhong 723001, People’s Republic of China
- Email: operatorguy@126.com
- Hong-Ke Du
- Affiliation: College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, People’s Republic of China
- Email: hkdu@snnu.edu.cn
- Hai-Yan Zhang
- Affiliation: College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, People’s Republic of China
- Received by editor(s): July 18, 2006
- Received by editor(s) in revised form: April 11, 2007
- Published electronically: May 30, 2008
- Additional Notes: This research was partially supported by the National Natural Science Foundation of China (10571113)
- Communicated by: Joseph A. Ball
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 136 (2008), 3483-3492
- MSC (2000): Primary 47A05, 46C07, 15A09
- DOI: https://doi.org/10.1090/S0002-9939-08-09194-6
- MathSciNet review: 2415032