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Path connectivity of idempotents on a Hilbert space
Author(s):
Yan-Ni
Chen;
Hong-Ke
Du;
Hai-Yan
Zhang
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3483-3492.
MSC (2000):
Primary 47A05, 46C07, 15A09
Posted:
May 30, 2008
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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.
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
DOI:
10.1090/S0002-9939-08-09194-6
PII:
S 0002-9939(08)09194-6
Keywords:
Idempotent,
orthogonal projection,
homotopic,
path connectivity
Received by editor(s):
July 18, 2006,
Received by editor(s) in revised form:
April 11, 2007
Posted:
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 of article:
Copyright
2008,
American Mathematical Society
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