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 language | English |
|---|---|
| Pages (from-to) | 325-333 |
| Number of pages | 9 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 379 |
| Issue number | 1 |
| DOIs | |
| State | Published - 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: [email protected] (S. Jung), [email protected] (E. Ko), [email protected] (M. Lee), [email protected] (J. Lee).
Keywords
- Complex symmetric operator
- Decomposable
- Dunford's property (C)
- Invariant subspaces
- Property (β)
- Weyl's theorem