Numerical ranges of radial Toeplitz operators on Bergman space

Kuo-Zhong Wang, Pei Yuan Wu

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

A Toeplitz operator TΦ with symbol Φ in L(D) on the Bergman space A2 (D), where D denotes the open unit disc, is radial if Φ(z) = Φ({pipe}z{pipe}) 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 TΦ with Φ harmonic on D and continuous on D̄ and radial Toeplitz operators are convexoid, but certain compact quasinilpotent Toeplitz operators are not.

Original languageEnglish
Pages (from-to)581-591
Number of pages11
JournalIntegral Equations and Operator Theory
Volume65
Issue number4
DOIs
StatePublished - 1 Dec 2009

Keywords

  • Bergman space
  • Convexoid operator
  • Numerical range
  • Radial Toeplitz operator

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