Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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THE RIESZ DECOMPOSITION THEOREM FOR SKEW SYMMETRIC OPERATORS

  • Zhu, Sen (Department of Mathematics Jilin University) ;
  • Zhao, Jiayin (Department of Mathematics Jilin University)
  • Received : 2014.06.01
  • Published : 2015.03.01
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Abstract

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 note, we explore the structure of skew symmetric operators with disconnected spectra. Using the classical Riesz decomposition theorem, we give a decomposition of certain skew symmetric operators with disconnected spectra. Several corollaries and illustrating examples are provided.

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