We discuss Toeplitz operators on Fock-Sobolev space with positive measure symbols.By FockCarleson measure,we obtain the characterizations for boundedness and compactness of Toeplitz operators.We also give some equival...We discuss Toeplitz operators on Fock-Sobolev space with positive measure symbols.By FockCarleson measure,we obtain the characterizations for boundedness and compactness of Toeplitz operators.We also give some equivalent conditions of Schatten p-class properties of Toeplitz operators by Berezin transform.展开更多
In this paper,some properties of Hardy-Sobolev spaces are obtained. The multipliers on these spaces are defined,and our results show that the multiplier algebra is more complex than that on the classical Hardy spaces....In this paper,some properties of Hardy-Sobolev spaces are obtained. The multipliers on these spaces are defined,and our results show that the multiplier algebra is more complex than that on the classical Hardy spaces. In addition,the spectrum theorem is obtained for some special multiplier.展开更多
The proof of the index formula of the Toeplitz operator with a continuous symbol on the Hardy space for the unit circle in the complex plane depends on the Hopftheorem. However,the analogue result of the Hopf theorem ...The proof of the index formula of the Toeplitz operator with a continuous symbol on the Hardy space for the unit circle in the complex plane depends on the Hopftheorem. However,the analogue result of the Hopf theorem does not hold on a general connected domain. Hence,the extension of the index formula of the Toeplitz operator on a general domain needs a method which is different from that for the case of the unit circle. In the present paper, the index formula of the Toeplitz operator with a continuous symbol on the finite complex connected domain in the complex plane is obtained, and the cohomology groups of Toeplitz algebras on general domains are discussed. In addition, the Toeplitz operators with symbols in QC are also discussed.展开更多
It is proved that if is a nonconstant bounded analytic function on the unit ball B n and continuous on S n in C n , and ψ is a bounded measurable function on S n such that T * and T ψ commute, then ψ is the bounda...It is proved that if is a nonconstant bounded analytic function on the unit ball B n and continuous on S n in C n , and ψ is a bounded measurable function on S n such that T * and T ψ commute, then ψ is the boundary value of an analytic function on B n . In addition, the commutants of two Toeplitz operators are also discussed.展开更多
This paper discusses the connectivity of the essential spectra of Toeplitz operators with symbols in H∞ +C on Hardy spaces and weighted Bergman spaces for several complex variables.
In this paper,the essential spectra of Toeplitz operators is discussed,and the K-theory of the Toeplitz algebra generated by {Tφ|φ∈C(iR)} is computed.In addition,the characteristic equation of Toeplitz operators is...In this paper,the essential spectra of Toeplitz operators is discussed,and the K-theory of the Toeplitz algebra generated by {Tφ|φ∈C(iR)} is computed.In addition,the characteristic equation of Toeplitz operators is obtained and the algebraic properties of Toeplitz operators are discussed.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos.11271092 and 11301101)Guangzhou Higher Education Science and Technology Project (Grant No.2012A018)
文摘We discuss Toeplitz operators on Fock-Sobolev space with positive measure symbols.By FockCarleson measure,we obtain the characterizations for boundedness and compactness of Toeplitz operators.We also give some equivalent conditions of Schatten p-class properties of Toeplitz operators by Berezin transform.
基金supported by National Natural Science Foundation of China(Grant No.11271092)Doctoral Fund of Ministry of Education of China(Grant No.20114410110001)
文摘In this paper,some properties of Hardy-Sobolev spaces are obtained. The multipliers on these spaces are defined,and our results show that the multiplier algebra is more complex than that on the classical Hardy spaces. In addition,the spectrum theorem is obtained for some special multiplier.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10371082).
文摘The proof of the index formula of the Toeplitz operator with a continuous symbol on the Hardy space for the unit circle in the complex plane depends on the Hopftheorem. However,the analogue result of the Hopf theorem does not hold on a general connected domain. Hence,the extension of the index formula of the Toeplitz operator on a general domain needs a method which is different from that for the case of the unit circle. In the present paper, the index formula of the Toeplitz operator with a continuous symbol on the finite complex connected domain in the complex plane is obtained, and the cohomology groups of Toeplitz algebras on general domains are discussed. In addition, the Toeplitz operators with symbols in QC are also discussed.
基金supported by National Natural Science Foundation of China (Grant Nos.110671041, 10971040)
文摘It is proved that if is a nonconstant bounded analytic function on the unit ball B n and continuous on S n in C n , and ψ is a bounded measurable function on S n such that T * and T ψ commute, then ψ is the boundary value of an analytic function on B n . In addition, the commutants of two Toeplitz operators are also discussed.
文摘This paper discusses the connectivity of the essential spectra of Toeplitz operators with symbols in H∞ +C on Hardy spaces and weighted Bergman spaces for several complex variables.
基金supported by National Natural Science Foundation of China (Grant No.10971040)the AV foundation of the Institute of Mathematical Sciences of Hong Kong Chinese University
文摘In this paper,the essential spectra of Toeplitz operators is discussed,and the K-theory of the Toeplitz algebra generated by {Tφ|φ∈C(iR)} is computed.In addition,the characteristic equation of Toeplitz operators is obtained and the algebraic properties of Toeplitz operators are discussed.
