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 -