Hyponormal Dual Toeplitz Operators on the Orthogonal Complement of the Harmonic Bergman Space
查看参考文献30篇
|
文摘
|
In this paper,we mainly study the hyponormality of dual Toeplitz operators on the orthogonal complement of the harmonic Bergman space.First we show that the dual Toeplitz operator with the bounded symbol is hyponormal if and only if it is normal.Then we obtain a necessary and sufficient condition for the dual Toeplitz operator S_ϕ with the symbol ϕ(z) = az~(n_1-m_1)+ bz~(n_2-m_2) (n_1,n_2,m_1,m_2 ∈ N and a,b ∈ C) to be hyponormal.Finally,we show that the rank of the commutator of two dual Toeplitz operators must be an even number if the commutator has a finite rank. |
|
来源
|
Acta Mathematica Sinica. English Series
,2023,39(5):846-862 【核心库】
|
|
DOI
|
10.1007/s10114-023-1382-9
|
|
关键词
|
Dual Toeplitz operator
;
harmonic Bergman space
;
normal
;
hyponormal
|
|
地址
|
1.
College of Mathematics and Physics,Wenzhou University, Wenzhou, 325035
2.
College of Mathematics and Statistics,Chongqing University, Chongqing, 401331
|
|
语种
|
英文 |
|
文献类型
|
研究性论文 |
|
ISSN
|
1439-8516 |
|
学科
|
数学 |
|
基金
|
supported by the Fundamental Research Funds for the Central Universities
;
国家自然科学基金
|
|
文献收藏号
|
CSCD:7465789
|
参考文献 共
30
共2页
|
|
1.
Arveson W.
A Short Course on Spectral Theory, Graduate Texts in Mathematics, Vol. 209,2000
|
CSCD被引
1
次
|
|
|
|
|
2.
Brown A. Algebraic properties of Toeplitz operators.
J. Reine Angew. Math,1964,213:89-102
|
CSCD被引
44
次
|
|
|
|
|
3.
Chen Y. Ranks of commutators of Toeplitz operators on the harmonic Bergman space.
Integral Equations Operator Theory,2013,75:31-38
|
CSCD被引
1
次
|
|
|
|
|
4.
Chen Y. Ranks of complex skew symmetric operators and applications to Toeplitz operators.
J. Math. Anal. Appl,2015,425:734-747
|
CSCD被引
2
次
|
|
|
|
|
5.
Chen Y. Dual Toeplitz Operators on Orthogonal Complement of the Harmonic Dirichlet Space.
Acta Math. Sin., Engl. Ser,2017,33:383-402
|
CSCD被引
2
次
|
|
|
|
|
6.
Choe B R. Commuting Toeplitz operators on the harmonic Bergman space.
Michigan Math. J,1999,46:163-174
|
CSCD被引
18
次
|
|
|
|
|
7.
Conway J B. A Course in Functional Analysis, Second Edition.
Graduate Texts in Mathematics, Vol. 96,1990
|
CSCD被引
1
次
|
|
|
|
|
8.
Cowen C C. Hyponormality of Toeplitz operators.
Proc. Amer. Math. Soc,1998,103:809-812
|
CSCD被引
6
次
|
|
|
|
|
9.
Cuckovic Z. A new necessary condition for the hyponormality of Toeplitz operators on the Bergman space.
J. Operator Theory,2018,79:287-300
|
CSCD被引
1
次
|
|
|
|
|
10.
Curto R E. Hyponormality and subnormality of block Toeplitz operators.
Adv. Math,2012,230:2094-2151
|
CSCD被引
2
次
|
|
|
|
|
11.
Ding X. Invertibility and spectral properties of dual Toeplitz operators.
J. Math. Anal. Appl,2020,484:1-18
|
CSCD被引
2
次
|
|
|
|
|
12.
Douglas R. Banach Algebra Techniques in Operator Theory, Second Edition.
Graduate Texts in Mathematics, Vol. 179,1998
|
CSCD被引
4
次
|
|
|
|
|
13.
Farenick D R. Hyponormality and spectra of Toeplitz operators.
Trans. Amer. Math. Soc,1996,348:4153-4174
|
CSCD被引
7
次
|
|
|
|
|
14.
Hwang I S. Hyponormal Toeplitz operators on the Bergman space II.
Bull. Korean Math. Soc,2007,44:517-522
|
CSCD被引
3
次
|
|
|
|
|
15.
Hwang I S. Hyponormal Toeplitz operators on the Bergman spaces.
J. Korean Math. Soc,2008,45:1027-1041
|
CSCD被引
1
次
|
|
|
|
|
16.
Hwang I S. Hyponormality of Toeplitz operators with polynomial symbols.
Math. Ann,1999,313:247-261
|
CSCD被引
2
次
|
|
|
|
|
17.
Le T. Hyponormality of Toeplitz operators on weighted Bergman space.
Integral Transforms Spec. Funct,2021,32:560-567
|
CSCD被引
1
次
|
|
|
|
|
18.
Lu Y. Commuting dual Toeplitz operators with pluriharmonic symbols.
J. Math. Anal. Appl,2005,302:149-156
|
CSCD被引
24
次
|
|
|
|
|
19.
Lu Y. Commuting dual Toeplitz operators on the polydisk.
Acta Math. Sin., Engl. Ser,2007,23:857-868
|
CSCD被引
8
次
|
|
|
|
|
20.
Lu Y. Hyponormal Toeplitz operators on the weighted Bergman space.
Integral Equations Operator Theory,2009,65:115-129
|
CSCD被引
4
次
|
|
|
|
|
了解气象卫星更多信息，请访问