Complex Symmetric Toeplitz Operators

被引：14

作者：

Bu, Qinggang ^{[1
]}

Chen, Yong ^{[2
]}

Zhu, Sen ^{[1
]}

机构：

[1] Jilin Univ, Dept Math, Changchun 130012, Peoples R China

[2] Hangzhou Normal Univ, Dept Math, Hangzhou 311121, Peoples R China

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2021年 / 93卷 / 02期

关键词：

Toeplitz operators; Hardy space; Complex symmetric operators;

D O I：

10.1007/s00020-021-02629-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper aims to study when a Toeplitz operator T-phi on the Hardy space H-2 of the unit disk is complex symmetric, that is, T-phi admits a symmetric matrix representation relative to some orthonormal basis of H-2. For certain trigonometric symbols., we give necessary and sufficient conditions for T-phi to be complex symmetric. In particular, we show that their complex symmetry coincides with the property "unitary equivalence to their transposes".

引用

页数：19

共 28 条

[1] Symbols of truncated Toeplitz operators
Baranov, Anton
Bessonov, Roman
Kapustin, Vladimir
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2011, 261 (12) : 3437 - 3456
[2] Bounded symbols and Reproducing Kernel Thesis for truncated Toeplitz operators
Baranov, Anton
Chalendar, Isabelle
Fricain, Emmanuel
Mashreghi, Javad
Timotin, Dan
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2010, 259 (10) : 2673 - 2701
[3] Truncated Toeplitz Operators: Spatial Isomorphism, Unitary Equivalence, and Similarity
Cima, Joseph A.
Garcia, Stephan Ramon
Ross, William T.
Wogen, Warren R.
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2010, 59 (02) : 595 - 620
[4] Dual truncated Toeplitz operators
Ding, Xuanhao
Sang, Yuanqi
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 461 (01) : 929 - 946
[5] Garcia S.R., 2013, Blaschke Products and Their Applications, V65, P265, DOI DOI 10.1007/978-1-4614-5341-315
[6] Garcia S.R., 2014, Oper. Theory Adv. Appl, P171
[7] Garcia S. R., 2016, INTRO MODEL SPACES T
[8] Garcia SR, 2006, CONTEMP MATH, V393, P67
[9] Complex symmetric operators and applications
Garcia, SR
Putinar, M
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 358 (03) : 1285 - 1315
[10] Garcia SR., 2013, OPER, V236, P181

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