Approximation of complex symmetric operators

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• 作者：Sen Zhu
• 关键词：47A55 ; 47A58 ; 47C10
• 刊名：Mathematische Annalen
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：364
• 期：1-2
• 页码：373-399
• 全文大小：575 KB
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• 作者单位：Sen Zhu (1)
  
  1. Department of Mathematics, Jilin University, 130012, Changchun, People’s Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1807

文摘

An operator \(T\) on a complex Hilbert space \(\mathcal {H}\) is called a complex symmetric operator if there exists a conjugate-linear, isometric involution \(C:\mathcal {H}\rightarrow \mathcal {H}\) so that \(CTC=T^*\). In this paper, we study the approximation of complex symmetric operators. By virtue of an intensive analysis of compact operators in singly generated \(C^*\)-algebras, we obtain a complete characterization of norm limits of complex symmetric operators and provide a classification of complex symmetric operators up to approximate unitary equivalence. This gives a general solution to the norm closure problem for complex symmetric operators. As an application, we provide a concrete description of partial isometries which are norm limits of complex symmetric operators. Mathematics Subject Classification 47A55 47A58 47C10