On complex symmetric operator matrices

Sungeun Jung, Eungil Ko, Ji Eun Lee

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

Abstract

An operator T∈L(H) is said to be complex symmetric if there exists a conjugation J on H such that T=JT*J. In this paper, we find several kinds of complex symmetric operator matrices and examine decomposability of such complex symmetric operator matrices and their applications. In particular, we consider the operator matrix of the form T=(AB0JA*J) where J is a conjugation on H. We show that if A is complex symmetric, then T is decomposable if and only if A is. Furthermore, we provide some conditions so that a-Weyl's theorem holds for the operator matrix T.

Original languageEnglish
Pages (from-to)373-385
Number of pages13
JournalJournal of Mathematical Analysis and Applications
Volume406
Issue number2
DOIs
StatePublished - 15 Oct 2013

Keywords

  • A-Weyl's theorem
  • Complex symmetric operator
  • Decomposable
  • Property (beta)

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