Frontiers of Mathematics in China >
Some results for operators on a model space
Received date: 17 Mar 2017
Accepted date: 12 Feb 2018
Published date: 28 Mar 2018
Copyright
We investigate some problems for truncated Toeplitz operators. Namely, the solvability of the Riccati operator equation on the set of all truncated Toeplitz operators on the model space Kθ = H2ΘθH2 is studied. We study in terms of Berezin symbols invertibility of model operators. We also prove some results for the Berezin number of the truncated Toeplitz operators. Moreover, we study some property for H2-functions in terms of noncyclicity of co-analytic Toeplitz operators and hypercyclicity of model operators.
Mehmet GÜRDAL , Ula¸s YAMANCI , Mübariz GARAYEV . Some results for operators on a model space[J]. Frontiers of Mathematics in China, 2018 , 13(2) : 287 -300 . DOI: 10.1007/s11464-018-0690-3
1 |
Bayart F, Matheron E. Dynamics of Linear Operators. Cambridge Univ Press, 2009
|
2 |
Berezin F A. Covariant and contravariant symbols for operators. Math USSR-Izv, 1972, 6: 1117–1151
|
3 |
Berezin F A. Quantization. Math USSR-Izv, 1974, 8: 1109–1163
|
4 |
Chalendar I, Fricain E, Gürdal M, Karaev M T. Compactness and Berezin symbols. Acta Sci Math (Szeged), 2012, 78: 315–329
|
5 |
Clark D. One dimensional perturbations of restricted shifts. J Anal Math, 1972, 25: 169–191
|
6 |
Englis M. Toeplitz operators and the Berezin transform on H2.Linear Algebra Appl, 1995, 223-224: 171–204
|
7 |
Gürdal M, S¸öhret F. Some results for Toeplitz operators on the Bergman space. Appl Math Comput, 2011, 218: 789–793
|
8 |
Karaev M T. Berezin symbols and Schatten-von Neumann classes. Math Notes, 2002, 72: 185–192
|
9 |
Karaev M T. Berezin symbol and invertibility of operators on the functional Hilbert spaces. J Funct Anal, 2006, 238: 181–192
|
10 |
Karaev M T. On the Riccati equations. Monatsh Math, 2008, 155: 161–166
|
11 |
Nikolski N K. Treatise on the Shift Operator.Heidelberg: Springer-Verlag, 1986
|
12 |
Sarason D. Algebraic properties of truncated Toeplitz operators. Oper Matrices, 2007, 1: 491–526
|
13 |
Wang X F, Xia J, Cao G F. Some properties of Toeplitz operators on Dirichlet space with respect to Berezin type transform. Sci Sin Math, 2012, 42(11): 1159–1170
|
14 |
Zhu K. Operator Theory in Function Spaces.2nd ed. Providence: Amer Math Soc, 2007
|
/
〈 | 〉 |