Abstract
In this paper, we study properties of weak crystal operators. In particular, we show that if T∈ L(H) is a complex symmetric operator, then T is weak crystal, crystal, or crystal-like if and only if T∗ is weak crystal, crystal, or crystal-like, respectively. Moreover, we prove that if T is a quasiaffinity, then T is weak crystal if and only if the Aluthge transform T~ (or the Duggal transform T~ D) of T is weak crystal. Finally, we give several applications of these results.
| Original language | English |
|---|---|
| Pages (from-to) | 1711-1727 |
| Number of pages | 17 |
| Journal | Banach Journal of Mathematical Analysis |
| Volume | 14 |
| Issue number | 4 |
| DOIs | |
| State | Published - 1 Sep 2020 |
Bibliographical note
Funding Information:Eungil Ko was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT)(2019R1F1A1058633). Ji Eun Lee was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2019R1A2C1002653). Eungil Ko and Mee-Jung Lee were supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2019R1A6A1A11051177).
Publisher Copyright:
© 2020, Tusi Mathematical Research Group (TMRG).
Keywords
- Aluthge transform
- Complex symmetric operator
- Crystal operator
- Crystal-like operator
- Invariant subspace
- Weak crystal operator