Approximate Unitary Equivalence to Skew Symmetric Operators
Approximate Unitary Equivalence to Skew Symmetric Operators
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DOI：
10.1007/s11785-014-0369-z
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发表时间：
2014-03
影响因子：
0.8
通讯作者：
Sen Zhu
中科院分区：
文献类型：
--
作者：
Sen Zhu
复Hilbert空间上的算子称为斜对称，如果可以表示为相对于某个标准正交基的斜对称矩阵。本文研究了斜对称算子的逼近问题，给出了斜对称算子的a-代数逼近。我们将满足条件的反对称算子分类到近似酉等价。这是用来表征时，一个单边加权移位与非零权重近似酉等价于一个反对称算子。
An operatoron a complex Hilbert spaceis called skew symmetric ifcan be represented as a skew symmetric matrix relative to some orthonormal basis for. In this paper, we study the approximation of skew symmetric operators and provide a-algebra approach to skew symmetric operators. We classify up to approximate unitary equivalence those skew symmetric operatorssatisfying. This is used to characterize when a unilateral weighted shift with nonzero weights is approximately unitarily equivalent to a skew symmetric operator.