Abstract
Numerical ranges of normal weighted composition operators on the Fock space of CN are completely characterized. The main result shows that numerical ranges of such operators are closely related to their composition symbols.
Highlights
Inspired by results on numerical ranges of composition operators on Hardy space [1], in this paper we give a complete characterization of numerical ranges of normal weighted composition operators on the Fock space of CN (N ≥ 1), the N-dimensional complex Euclidean space
The Fock space F2 over CN is the space of analytic functions f on CN with
Let T be a bounded operator on a complex Hilbert space
Summary
In [3], normal weighted composition operators on F2 are characterized completely. In [4], the spectrum of normal weighted composition operators on F2 is considered. For more results on numerical ranges of (weighted) composition operators on Hardy space, see [5,6,7,8].
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