Abstract
In this paper, we study several properties of m-complex symmetric operators. In particular, we prove that if T ε L(H) is an m-complex symmetric operator and N is a nilpotent operator of order n > 2 with TN = NT, then T + N is a (2n+m-2)-complex symmetric operator. Moreover, we investigate the decomposability of T+A and TA where T is an m-complex symmetric operator and A is an algebraic operator. Finally, we provide various spectral relations of such operators. As some applications of these results, we discuss Weyl type theorems for such operators.
| Original language | English |
|---|---|
| Pages (from-to) | 233-248 |
| Number of pages | 16 |
| Journal | Studia Universitatis Babes-Bolyai Mathematica |
| Volume | 62 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2017 |
Bibliographical note
Funding Information:This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(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(2016R1A2B4007035) and this research is partially supported by Grant-in-Aid Scientific Research No.15K04910.
Keywords
- Conjugation
- Decomposable
- Nilpotent perturbations
- Weyl type theorems
- m-complex symmetric operator