TY - JOUR
T1 - Crystal complex symmetric operators
AU - Ko, Eungil
AU - Lee, Ji Eun
AU - Lee, Mee Jung
N1 - Funding Information:
Eungil Ko was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT)(2019R1F1A1058633). Ji Eun Lee 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). Eungil Ko and Mee-Jung Lee were supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2019R1A6A1A11051177).
Publisher Copyright:
© 2020, Tusi Mathematical Research Group (TMRG).
PY - 2020/9/1
Y1 - 2020/9/1
N2 - 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.
AB - 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.
KW - Aluthge transform
KW - Complex symmetric operator
KW - Crystal operator
KW - Crystal-like operator
KW - Invariant subspace
KW - Weak crystal operator
UR - http://www.scopus.com/inward/record.url?scp=85087299164&partnerID=8YFLogxK
U2 - 10.1007/s43037-020-00078-7
DO - 10.1007/s43037-020-00078-7
M3 - Article
AN - SCOPUS:85087299164
SN - 1735-8787
VL - 14
SP - 1711
EP - 1727
JO - Banach Journal of Mathematical Analysis
JF - Banach Journal of Mathematical Analysis
IS - 4
ER -