TY - JOUR
T1 - On operators T commuting with CTC where C is a conjugation
AU - Chō, Muneo
AU - Ko, Eungil
AU - Lee, Ji Eun
N1 - Funding Information:
This work is supported by Grant-in-Aid Scientific Research No.15K04910. The second author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(2016R1D1A1B03931937). 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(2019R1A2C1002653).
Publisher Copyright:
© 2020 Korean Mathematical Society.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Complex symmetric operator
KW - Conjugation operator
KW - Normal operator
UR - http://www.scopus.com/inward/record.url?scp=85078780834&partnerID=8YFLogxK
U2 - 10.4134/BKMS.b190054
DO - 10.4134/BKMS.b190054
M3 - Article
AN - SCOPUS:85078780834
SN - 1015-8634
VL - 57
SP - 69
EP - 79
JO - Bulletin of the Korean Mathematical Society
JF - Bulletin of the Korean Mathematical Society
IS - 1
ER -