The class of complex symmetric operators is not norm closed
The class of complex symmetric operators is not norm closed
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DOI：
10.1090/s0002-9939-2011-11345-5
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发表时间：
2012-05
期刊：
影响因子：
--
通讯作者：
Sen Zhu;Chun Guang Li;Y. Ji
中科院分区：
文献类型：
--
作者：
Sen Zhu;Chun Guang Li;Y. Ji
. An operator T ∈ B ( H ) is complex symmetric if there exists a conjugate-linear, isometric involution C : H −→ H so that CTC = T ∗ . In this paper, a class of complex symmetric operators on finite dimensional Hilbert spaces is constructed. As an application, it is shown that Kakutani’s unilateral weighted shift operator is not complex symmetric; however, it is a norm limit of complex symmetric operators. This gives a negative answer to a question of S. Garcia and W. Wogen: that is, whether or not the class of complex symmetric operators is norm closed.
