Abstract.
In this paper, we reprove that: (i) the Aluthge transform of a complex symmetric operator \(\tilde{T} = |T|^{\frac{1}{2}} U|T|^{\frac{1}{2}}\) is complex symmetric, (ii) if T is a complex symmetric operator, then \((\tilde{T})^{*}\) and \(\widetilde{T^{*}}\) are unitarily equivalent. And we also prove that: (iii) if T is a complex symmetric operator, then \(\widetilde{(T^{*})}_{s,t}\) and \((\tilde{T}_{t,s})^{*}\) are unitarily equivalent for s, t > 0, (iv) if a complex symmetric operator T belongs to class wA(t, t), then T is normal.
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This work was supported by National Natural Science Fund of China (10771011) and National Key Basic Research Project of China (2005CB321902).
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Wang, X., Gao, Z. A Note on Aluthge Transforms of Complex Symmetric Operators and Applications. Integr. equ. oper. theory 65, 573 (2009). https://doi.org/10.1007/s00020-009-1719-5
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DOI: https://doi.org/10.1007/s00020-009-1719-5