THE RIESZ DECOMPOSITION THEOREM FOR SKEW SYMMETRIC OPERATORS

Title & Authors
THE RIESZ DECOMPOSITION THEOREM FOR SKEW SYMMETRIC OPERATORS
Zhu, Sen; Zhao, Jiayin;

Abstract
An operator T on a complex Hilbert space $\small{\mathcal{H}}$ is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for $\small{\mathcal{H}}$. 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;spectrum;
Language
English
Cited by
1.
ON SKEW SYMMETRIC OPERATORS WITH EIGENVALUES,;

대한수학회지, 2015. vol.52. 6, pp.1271-1286
1.
ON SKEW SYMMETRIC OPERATORS WITH EIGENVALUES, Journal of the Korean Mathematical Society, 2015, 52, 6, 1271
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