On scalar extensions and spectral decompositions of complex symmetric operators |
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| Authors: | Sungeun Jung |
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| Affiliation: | a Department of Mathematics, Ewha Womans University, Seoul 120-750, Republic of Korea
b Institute of Mathematical Sciences, Ewha Womans University, Seoul 120-750, Republic of Korea |
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| Abstract: | In this paper we prove that a complex symmetric operator with property (δ) is subscalar. As a corollary, we get that such operators with rich spectra have nontrivial invariant subspaces. We also provide various relations for spectral decomposition properties between complex symmetric operators and their adjoints. |
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| Keywords: | Complex symmetric operator Property (δ) Decomposable Subscalar Spectral decompositions |
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