Properties of complex symmetric operators

Sungeun Jung, Eungil Ko, Ji Eun Lee

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


An operator T ∈L(H) is said to be complex symmetric if there exists a conjugation C on H such that T =CT∗C. In this paper, we prove that every complex symmetric operator is biquasitriangular. Also, we show that if a complex symmetric operator T is weakly hypercyclic, then both T and T∗ have the single-valued extension property and that if T is a complex symmetric operator which has the property (δ), then Weyl’s theorem holds for f (T) and f (T)∗ where f is any analytic function in a neighborhood of σ (T). Finally, we establish equivalence relations among Weyl type theorems for complex symmetric operators.

Original languageEnglish
Pages (from-to)957-958
Number of pages2
JournalOperators and Matrices
Issue number4
StatePublished - 1 Dec 2014

Bibliographical note

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© 2014, Element D.O.O. All rights reserved.


  • Biquasitriangular
  • Complex symmetric operator
  • Weakly hypercyclic
  • Weyl type theorem


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