In this paper, we investigate the Toeplitz operators with positive measure symbols on the Bergman spaces of bounded multi-connected domains and show that a Toeplitz operator is bounded or compact if and only if the sy...In this paper, we investigate the Toeplitz operators with positive measure symbols on the Bergman spaces of bounded multi-connected domains and show that a Toeplitz operator is bounded or compact if and only if the symbol measure is a Carleson or vanishing Carleson measure respectively.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
基金This work was supported by the NSF (19971061) of China and the Science Foundation ofFushun Petroleum Institute.
文摘In this paper, we investigate the Toeplitz operators with positive measure symbols on the Bergman spaces of bounded multi-connected domains and show that a Toeplitz operator is bounded or compact if and only if the symbol measure is a Carleson or vanishing Carleson measure respectively.
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.
