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
Publisher Copyright:© 2020, Tusi Mathematical Research Group (TMRG).
Keywords
- Aluthge transform
- Complex symmetric operator
- Crystal operator
- Crystal-like operator
- Invariant subspace
- Weak crystal operator