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 language | English |
|---|---|
| Pages (from-to) | 373-385 |
| Number of pages | 13 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 406 |
| Issue number | 2 |
| DOIs | |
| State | Published - 15 Oct 2013 |
Bibliographical note
Funding Information:The authors wish to thank the referee for a careful reading and valuable comments for the original draft. This work was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2009-0093827 ). The third author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2012R1A1A3006841 ).
Keywords
- A-Weyl's theorem
- Complex symmetric operator
- Decomposable
- Property (beta)