Abstract
In this paper, we study the properties of T satisfying [CT C, T ] = 0 for some conjugation C where [R, S]:= RS − SR. In particular, we show that if T is normal, then [CT C, C] = 0. Moreover, the class of operators T satisfy [CT C, T ] = 0 is norm closed. Finally, we prove that if T is complex symmetric, then T is binormal if and only if [C|T |C, |T |] = 0.
Original language | English |
---|---|
Pages (from-to) | 69-79 |
Number of pages | 11 |
Journal | Bulletin of the Korean Mathematical Society |
Volume | 57 |
Issue number | 1 |
DOIs | |
State | Published - 2020 |
Bibliographical note
Publisher Copyright:© 2020 Korean Mathematical Society.
Keywords
- Complex symmetric operator
- Conjugation operator
- Normal operator