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

 

Skew symmetric normal operators


Authors: Chun Guang Li and Sen Zhu
Journal: Proc. Amer. Math. Soc. 141 (2013), 2755-2762
MSC (2010): Primary 47B25, 47B15; Secondary 47A65
Published electronically: April 8, 2013
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Abstract: An operator $ T$ on a complex Hilbert space $ \mathcal {H}$ is said to be skew symmetric if there exists a conjugate-linear, isometric involution $ C:\mathcal {H}\longrightarrow \mathcal {H}$ so that $ CTC=-T^*$. In this paper, we shall give two structure theorems for skew symmetric normal operators.


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Additional Information

Chun Guang Li
Affiliation: Institute of Mathematics, Jilin University, Changchun 130012, People’s Republic of China
Email: licg09@mails.jlu.edu.cn

Sen Zhu
Affiliation: Department of Mathematics, Jilin University, Changchun 130012, People’s Republic of China
Address at time of publication: School of Mathematical Sciences, Fudan University, 220 Handan Road, Shanghai 200433, People’s Republic of China
Email: zhusen@jlu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11759-4
PII: S 0002-9939(2013)11759-4
Keywords: Skew symmetric operators, complex symmetric operators, normal operators
Received by editor(s): September 17, 2011
Received by editor(s) in revised form: October 30, 2011
Published electronically: April 8, 2013
Additional Notes: This work was supported by NNSF of China (11101177, 10971079, 11271150), China Postdoctoral Science Foundation (2011M500064, 2012T50392), Shanghai Postdoctoral Scientific Program (12R21410500), and Science Foundation for Young Teachers of Northeast Normal University (12QNJJ001)
The authors wish to thank the editor and the referee for many helpful comments and suggestions which greatly improved the manuscript
Communicated by: Marius Junge
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.