J. Korean Math. Soc. 2015; 52(2): 403-416
Printed March 1, 2015
https://doi.org/10.4134/JKMS.2015.52.2.403
Copyright © The Korean Mathematical Society.
Sen Zhu and Jiayin Zhao
Jilin University, Jilin University
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.
Keywords: skew symmetric operator, complex symmetric operator, spect\-rum
MSC numbers: Primary 47A10, 47B99; Secondary 47A05
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