Complex symmetric weighted shifts
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- by Sen Zhu and Chun Guang Li PDF
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Abstract:
An operator $T$ on a complex Hilbert space $\mathcal {H}$ is said to be complex symmetric if there exists a conjugate-linear, isometric involution $C:\mathcal {H}\longrightarrow \mathcal {H}$ so that $CTC=T^*$. In this paper, it is completely determined when a scalar (unilateral or bilateral) weighted shift is complex symmetric. In particular, we give a canonical decomposition of weighted shifts with complex symmetry. Also we characterize those weighted shifts for which complex symmetry is invariant under generalized Aluthge transforms. As an application, we give a negative answer to a question of S. Garcia.References
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Additional Information
- 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, Shanghai 200433, People’s Republic of China
- Email: senzhu@163.com
- Chun Guang Li
- Affiliation: Institute of Mathematics, Jilin University, Changchun 130012, People’s Republic of China
- Email: licg09@mails.jlu.edu.cn
- Received by editor(s): April 8, 2011
- Received by editor(s) in revised form: May 27, 2011
- Published electronically: July 25, 2012
- Additional Notes: This work was partially supported by NNSF of China (11101177, 11026038, 10971079), China Postdoctoral Science Foundation (2011M500064) and Shanghai Postdoctoral Scientific Program (12R21410500)
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 511-530
- MSC (2010): Primary 47B37, 47A05; Secondary 47A66
- DOI: https://doi.org/10.1090/S0002-9947-2012-05642-X
- MathSciNet review: 2984066