Title: Numerical Ranges of Radial Toeplitz Operators on Bergman Space
Authors: Wang, Kuo Zhong
Wu, Pei Yuan
應用數學系
Department of Applied Mathematics
Keywords: Numerical range;radial Toeplitz operator;Bergman space;convexoid operator
Issue Date: 1-Dec-2009
Abstract: 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.
URI: http://dx.doi.org/10.1007/s00020-009-1713-y
http://hdl.handle.net/11536/6380
ISSN: 0378-620X
DOI: 10.1007/s00020-009-1713-y
Journal: INTEGRAL EQUATIONS AND OPERATOR THEORY
Volume: 65
Issue: 4
Begin Page: 581
End Page: 591
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