On scalar extensions and spectral decompositions of complex symmetric operators

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...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 384; no. 2; pp. 252 - 260
Main Authors Jung, Sungeun, Ko, Eungil, Lee, Ji Eun
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 15.12.2011
Elsevier
Subjects
Complex symmetric operator
Decomposable
Exact sciences and technology
Mathematical analysis
Mathematics
Operator theory
Property ( δ)
Sciences and techniques of general use
Spectral decompositions
Subscalar
Complex symmetric operator
Property ( δ)
Spectral decompositions
Decomposable
Subscalar
Spectral operator
Invariant subspace
Mathematical analysis
Spectral properties
Property (δ)
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Summary: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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2011.05.056