Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON SKEW SYMMETRIC OPERATORS WITH EIGENVALUES

  • ZHU, SEN (DEPARTMENT OF MATHEMATICS JILIN UNIVERSITY)
  • Received : 2015.01.04
  • Published : 2015.11.01
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Abstract

An operator T on a complex Hilbert space H is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for H. In this paper, we study skew symmetric operators with eigenvalues. First, we provide an upper-triangular operator matrix representation for skew symmetric operators with nonzero eigenvalues. On the other hand, we give a description of certain skew symmetric triangular operators, which is based on the geometric relationship between eigenvectors.

Keywords

Acknowledgement

Supported by : National Science Foundation of China

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