Browsing by Author "Wang, Kuo Zhong"

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Numerical Ranges of Radial Toeplitz Operators on Bergman Space
(2009-12-01)
Wang, Kuo Zhong
;
Wu, Pei Yuan
;
應用數學系
;
Department of Applied Mathematics
A Toeplitz operator T(phi) with symbol phi in L(infinity)(D) on the Bergman space A(2)(D), where D denotes the open unit disc, is radial if phi(z) = phi(vertical bar z vertical bar) a. e. on D. In this paper, we consider the numerical ranges of such operators. It is shown that all finite line segments, convex hulls of analytic images of D and closed convex polygonal regions in the plane are the numerical ranges of radial Toeplitz operators. On the other hand, Toeplitz operators T(phi) with phi harmonic on D and continuous on (D) over bar and radial Toeplitz operators are convexoid, but certain compact quasinilpotent Toeplitz operators are not.