Abstract
In this paper, we prove that if \(T\in {\mathcal {L}({\mathcal {H}})}\) is complex symmetric, then its generalized mean transform \({\widehat{T}}(t)~ (t\not =0)\) of T is also complex symmetric. Next, we consider complex symmetry property of the mean transform \({\widehat{T}}(0)\) of truncated weighted shift operators. Finally, we study properties of the generalized mean transform of skew complex symmetric operators.
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Acknowledgements
The authors wish to thank the referees for their invaluable comments on the original draft. C. Benhida was partially supported by Labex CEMPI (ANR-11-LABX-0007-01). M. Chō is partially supported by Grant-in-Aid Scientific Research no. 15K04910. E. Ko was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1F1A1058633). J. E. Lee was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1A2C1002653).
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Communicated by David Larson.
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Benhida, C., Chō, M., Ko, E. et al. On the generalized mean transforms of complex symmetric operators. Banach J. Math. Anal. 14, 842–855 (2020). https://doi.org/10.1007/s43037-019-00041-1
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DOI: https://doi.org/10.1007/s43037-019-00041-1