Approximate Unitary Equivalence to Skew Symmetric Operators

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• 作者：Sen Zhu (1)
  
• 关键词：Skew symmetric operators ; Approximate unitary equivalence ; Approximation ; Weighted shifts ; Primary 47A58 ; 47A45 ; Secondary 47B99 ; 47C15
• 刊名：Complex Analysis and Operator Theory
• 出版年：2014
• 出版时间：October 2014
• 年：2014
• 卷：8
• 期：7
• 页码：1565-1580
• 全文大小：241 KB
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• 作者单位：Sen Zhu (1)
  
  1. Department of Mathematics, Jilin University, Changchun聽, 130012, People鈥檚 Republic of China
  
• ISSN：1661-8262

文摘

An operator \(T\) on a complex Hilbert space \(\mathcal {H}\) is called skew symmetric if \(T\) can be represented as a skew symmetric matrix relative to some orthonormal basis for \(\mathcal {H}\) . In this paper, we study the approximation of skew symmetric operators and provide a \(C^*\) -algebra approach to skew symmetric operators. We classify up to approximate unitary equivalence those skew symmetric operators \(T\in \mathcal {B(H)}\) satisfying \(C^*(T)\cap \mathcal {K(H)}=\{0\}\) . This is used to characterize when a unilateral weighted shift with nonzero weights is approximately unitarily equivalent to a skew symmetric operator.