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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Invertibility of linear combinations of two idempotents


Authors: Hongke Du, Xiyan Yao and Chunyuan Deng
Journal: Proc. Amer. Math. Soc. 134 (2006), 1451-1457
MSC (2000): Primary 47A05, 47L07
Published electronically: October 18, 2005
MathSciNet review: 2199192
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Abstract: Let $ P$ and $ Q$ be two idempotents on a Hilbert space. In this note, we prove that the invertibility of the linear combination $ \lambda_1P+\lambda_2Q$ is independent of the choice of $ \lambda _i$, $ i=1,2,$ if $ \lambda_1\lambda_2\neq 0$ and $ \lambda_1+\lambda_2\neq 0.$


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Additional Information

Hongke Du
Affiliation: College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, People’s Republic of China
Email: hkdu@snnu.edu.cn

Xiyan Yao
Affiliation: College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, People’s Republic of China
Email: yaoxiyan63@163.com

Chunyuan Deng
Affiliation: College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, People’s Republic of China
Email: cy-deng@263.net

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08091-3
PII: S 0002-9939(05)08091-3
Keywords: Idempotent, invertibility, linear combination of two idempotents
Received by editor(s): June 19, 2004
Received by editor(s) in revised form: December 20, 2004
Published electronically: October 18, 2005
Additional Notes: This research was partially supported by the National Natural Science Foundation of China (19771056)
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.