TY - JOUR
T1 - On properties of C-normal operators II
AU - Ko, Eungil
AU - Lee, Ji Eun
AU - Lee, Mee Jung
N1 - Funding Information:
The authors wish to thank the editor for a careful reading and valuable comments and suggestions for the original draft. Eungil Ko was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (2019R1F1A1058633). Ji Eun Lee was supported by the National Research Foundation of Korea(NRF) grant funded by the Korean government (MSIT) (No. 2022R1H1A2091052). Mee-Jung Lee was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2020R1I1A1A01064575).
Publisher Copyright:
© 2023, Tusi Mathematical Research Group (TMRG).
PY - 2023/4
Y1 - 2023/4
N2 - For T∈ L(H) , an operator T is called C-normal if (CT) #CT= CT(CT) # for a conjugation C on H. In this paper, we continue our study, begun in Ko et al. (Banach J. Math. Anal. 14:1711–1727, 2020), of various properties of C-normal operators. Especially, we prove that if T= U| T| is the polar decomposition of T, C is a conjugation on H with U∗CU∗= C, and T is C-normal, then T∗ possess the property (β) , the single valued extension property, the property (C) if and only if T possess, respectively. In addition, if T is C-normal, then T is binormal if and only if | T| n and C| T| mC commute for everyl positive integers m, n.
AB - For T∈ L(H) , an operator T is called C-normal if (CT) #CT= CT(CT) # for a conjugation C on H. In this paper, we continue our study, begun in Ko et al. (Banach J. Math. Anal. 14:1711–1727, 2020), of various properties of C-normal operators. Especially, we prove that if T= U| T| is the polar decomposition of T, C is a conjugation on H with U∗CU∗= C, and T is C-normal, then T∗ possess the property (β) , the single valued extension property, the property (C) if and only if T possess, respectively. In addition, if T is C-normal, then T is binormal if and only if | T| n and C| T| mC commute for everyl positive integers m, n.
KW - Binormal
KW - C-normal operator
KW - The property (C)
KW - The property (β)
UR - http://www.scopus.com/inward/record.url?scp=85146585064&partnerID=8YFLogxK
U2 - 10.1007/s43034-022-00246-w
DO - 10.1007/s43034-022-00246-w
M3 - Article
AN - SCOPUS:85146585064
SN - 2008-8752
VL - 14
JO - Annals of Functional Analysis
JF - Annals of Functional Analysis
IS - 2
M1 - 29
ER -