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.

中文翻译：

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关于复对称算子的广义均值变换

在本文中，我们证明如果 $$T\in {\mathcal {L}({\mathcal {H}})}$$ 是复对称的，那么它的广义均值变换 $${\widehat{T}}( t)~ (t\not =0)$$ 的 T 也是复对称的。接下来，我们考虑截断加权移位运算符的均值变换 $${\widehat{T}}(0)$$ 的复杂对称性。最后，我们研究了偏斜复对称算子的广义平均变换的性质。