On local spectral properties of complex symmetric operators

S. Jung, E. Ko, M. Lee, J. Lee

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Abstract

In this paper we study properties of complex symmetric operators. In particular, we prove that every complex symmetric operator having property (β) or (δ) is decomposable. Moreover, we show that complex symmetric operator T has Dunford's property (C) and it satisfies Weyl's theorem if and only if its adjoint does.

Original languageEnglish
Pages (from-to)325-333
Number of pages9
JournalJournal of Mathematical Analysis and Applications
Volume379
Issue number1
DOIs
StatePublished - 1 Jul 2011

Bibliographical note

Funding Information:
✩ This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) grant funded by the Korean Government (MEST) (2009-0093125). The forth author was supported by the National Research Foundation of Korea grant funded by the Korean Government (Ministry of Education, Science and Technology) [KRF-2010-355-C00005]. * Corresponding author. E-mail addresses: ssung105@ewhain.net (S. Jung), eiko@ewha.ac.kr (E. Ko), meejung@ewhain.net (M. Lee), jieun7@ewhain.net (J. Lee).

Keywords

  • Complex symmetric operator
  • Decomposable
  • Dunford's property (C)
  • Invariant subspaces
  • Property (β)
  • Weyl's theorem

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