Abstract
Let \(\mathcal {H}\) be a complex Hilbert space. In this note, we consider the following interpolation problem: characterize the class of pairs (P, Q) of positive operators on \(\mathcal {H}\) satisfying \(CPC=Q\) for some conjugation C on \({\mathcal {H}}\). We give a solution to the problem in the case that P and Q are simultaneously diagonal operators. As an application, we give a concrete characterization for a (unilateral or bilateral) weighted shift to possess a generalized symmetry introduced by Ptak et al. (Electron. J Linear Algebra 36, 67–79, 2020).
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant numbers 12171195, 12101114) and China Postdoctoral Science Foundation (Grant number 2020M681024). The authors wish to express their thanks to the referee for several helpful comments and constructive suggestions concerning the manuscript.
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Liu, T., Xie, X. & Zhu, S. An Interpolation Problem for Conjugations II. Mediterr. J. Math. 19, 153 (2022). https://doi.org/10.1007/s00009-022-02080-9
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DOI: https://doi.org/10.1007/s00009-022-02080-9