In this paper, we study unbounded complex symmetric Toeplitz operators on the Hardy space $H^{2}(\mathbb{D})$ and the Fock space $\mathscr{F}^{2}$. The technique used to investigate the complex symmetry of unbounded Toeplitz operators is different from that used to investigate the complex symmetry of bounded Toeplitz operators.
Kaikai HAN
,
Maofa WANG
,
Qi WU
. UNBOUNDED COMPLEX SYMMETRIC TOEPLITZ OPERATORS[J]. Acta mathematica scientia, Series B, 2022
, 42(1)
: 420
-428
.
DOI: 10.1007/s10473-022-0123-y
[1] Garcia S, Putinar M. Complex symmetric operators and applications II. Trans Amer Math Soc, 2007, 359(8):3913-3931
[2] Guo K, Zhu S. A canonical decomposition of complex symmetric operators. J Operator Theory, 2014, 72(2):529-547
[3] Janas J. Unbounded Toeplitz operators in the Bargmann-Segal space. Studia Math, 1991, 99(2):87-99
[4] Janas J, Stochel J. Unbounded Toeplitz operators in the Segal-Bargmann space II. J Funct Anal, 1994, 126(2):418-447
[5] Jiang C, Dong X, Zhou Z. Complex symmetric Toeplitz operators on the unit polydisk and the unit ball. Acta Math Sci, 2020, 40B(1):35-44
[6] Ko E, Lee J. On complex symmetric Toeplitz operators. J Math Anal Appl, 2016, 434(1):20-34
[7] Ko E, Lee J. Hyponormality of Toeplitz operators on the Fock spaces. Complex Var Elliptic Equ, 2019, 64(11):1825-1843
[8] Li A, Liu Y, Chen Y. Complex symmetric Toeplitz operators on the Dirichlet space. J Math Anal Appl, 2020, 487(1):123998, 12pp
[9] Martínez-Avendaño R A, Rosenthal P. An introduction to operators on the Hardy-Hilbert space. New York:Springer, 2007
[10] Noor S. Complex symmetry of Toeplitz operators with continuous symbols. Arch Math (Basel), 2017, 109(5):455-460
[11] Sarason D. Unbounded Toeplitz operators. Integral Equations Operator Theory, 2008, 61(2):281-298
