By using commutative C*-algebra techniques, spectrum and essential spectrum of normal weighted composition operators on the Fock space over CN are completely characterized. As an application, spectrum of self-adjoint ...By using commutative C*-algebra techniques, spectrum and essential spectrum of normal weighted composition operators on the Fock space over CN are completely characterized. As an application, spectrum of self-adjoint weighted composition operators on the Fock space are obtained also.展开更多
In this paper, we study Toeplitz operators with harmonic symbols on the harmonic Dirichlet space, and show that the product of two Toeplitz operators is another Toeplitz operator only if one factor is constant.
In this paper, we show that a multiplication operator on the Dirichlet space D is unitarily equivalent to Dirichlet shift of multiplicity n ＋ 1 （n ≥ 0） if and only if its symbol is c zn＋1 for some constant c. The...In this paper, we show that a multiplication operator on the Dirichlet space D is unitarily equivalent to Dirichlet shift of multiplicity n ＋ 1 （n ≥ 0） if and only if its symbol is c zn＋1 for some constant c. The result is very different from the cases of both the Bergman space and the Hardy space.展开更多
This paper gives a note on weighted composition operators on the weighted Bergman space, which shows that for a fixed composition symbol, the weighted composition operators are bounded on the weighted Bergman space on...This paper gives a note on weighted composition operators on the weighted Bergman space, which shows that for a fixed composition symbol, the weighted composition operators are bounded on the weighted Bergman space only with bounded weighted symbols if and only if the composition symbol is a finite Blaschke product.展开更多
基金Supported by NSFC(Grant Nos.11771401 and 11471189)
文摘By using commutative C*-algebra techniques, spectrum and essential spectrum of normal weighted composition operators on the Fock space over CN are completely characterized. As an application, spectrum of self-adjoint weighted composition operators on the Fock space are obtained also.
基金Supported by Tianyuan Funds of China (Grant No. 10926143)YSF of Shanxi Province (Grant No. 20100210022)+1 种基金partially supported by NSFC (Grant No. 10971195)NSF of Zhejiang Province (Grant Nos. Y6090689, Y6110260)
文摘In this paper, we study Toeplitz operators with harmonic symbols on the harmonic Dirichlet space, and show that the product of two Toeplitz operators is another Toeplitz operator only if one factor is constant.
基金Supported by Tianyuan Foundation of China (Grant No. 10926143)Young Science Foundation of Shanxi Province(Grant No. 2010021002-2)+2 种基金the National Natural Science Foundation of China (Grant No. 10971195)the Natural Science Foundation of Zhejiang Province (Grant Nos. Y6090689 Y6110260)
文摘In this paper, we show that a multiplication operator on the Dirichlet space D is unitarily equivalent to Dirichlet shift of multiplicity n ＋ 1 （n ≥ 0） if and only if its symbol is c zn＋1 for some constant c. The result is very different from the cases of both the Bergman space and the Hardy space.
基金Supported by NSFC(Grant Nos.11201274,11171245,11471189)a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘This paper gives a note on weighted composition operators on the weighted Bergman space, which shows that for a fixed composition symbol, the weighted composition operators are bounded on the weighted Bergman space only with bounded weighted symbols if and only if the composition symbol is a finite Blaschke product.
