| Toeplitz operators on connected domains" |
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| 作者姓名： | CAO Guangfu School of Mathematics and Information Sciences Guangzhou University Guangzhou China |
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| 作者单位： | CAO Guangfu School of Mathematics and Information Sciences，Guangzhou University，Guangzhou 510006，China |
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| 基金项目： | 国家高技术研究发展计划(863计划) |
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| 摘 要： | 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 Hopf theorem. 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.
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| 收稿时间： | 14 September 2005 |
| 修稿时间： | 28 December 2005 |
Toeplitz operators on connected domains |
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| CAO Guangfu School of Mathematics and Information Sciences,Guangzhou University,Guangzhou ,China.Toeplitz operators on connected domains"[J].Science in China(Mathematics),2006,49(6):827-837. |
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| Authors: | CAO Guangfu |
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| Institution: | School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China |
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| Abstract: | 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 Hopf theorem. 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. |
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| Keywords: | connected domain Toeplitz operator |
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