Spectrum and essential spectrum of Toeplitz operators

Dechao Zheng  (Vanderbilt University & Chongqing University)

9:30 am to 10:30 am, August 8th, 2012    Science Building A1510




Abstract:

On the Hardy space, by means of an elegant and ingenious argument, Widom showed that the spectrum of a bounded Toeplitz operator is always connected and Douglas showed that the essential spectrum of a bounded Toeplitz operator is also connected. On the Bergman space, in 1979, G. McDonald and the C. Sundberg showed that the essential spectrum of T' is connected for ' a harmonic function on the unit disk which is either real or piecewise continuous on the boundary. They asked whether the essential spectrum of a Toeplitz operator on the Bergman space with bounded harmonic symbol is connected.

In this talk, we will show an example that the spectrum and the essential spectrum of a Toeplitz operator with bounded harmonic symbol is disconnected.

This is a joint work with Carl Sundberg.

About the speaker:

郑德超教授是国际著名数学家,函数空间上的算子理论研究领域的领军人物。郑德超教授现任重庆大学两江数学中心主任,博士生导师,国家千人计划获得者。

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