Approximate Unitary Equivalence to Skew Symmetric Operators

作者：Zhu, Sen^*

来源：Complex Analysis and Operator Theory, 2014, 8(7): 1565-1580.

DOI：10.1007/s11785-014-0369-z

• Skew symmetric operators
• Approximate unitary equivalence
• Approximation
• Weighted shifts

An operator on a complex Hilbert space is called skew symmetric if can 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 operators satisfying . This is used to characterize when a unilateral weighted shift with nonzero weights is approximately unitarily equivalent to a skew symmetric operator.

• 出版日期2014-10
• 单位吉林大学