Numerical range of weighted composition operators on the Fock space

被引：0

作者：

Shaabani, Mahmood Haji ^{[1
]}

Fatehi, Mahsa ^{[2
]}

Hammond, Christopher N. B. ^{[3
]}

机构：

[1] Shiraz Univ Technol, Dept Math, Shiraz, Iran

[2] Islamic Azad Univ, Dept Math, Shiraz Branch, Shiraz, Iran

[3] Connecticut Coll, Dept Math & Stat, New London, CT 06320 USA

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2022年 / 67卷 / 06期

关键词：

Fock space; weighted composition operator; numerical range;

D O I：

10.1080/17476933.2021.1890053

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the numerical range of a bounded weighted composition operator C-psi,C-phi on the Fock space F-2, where the entire function phi must have the form az + b with a and b in az + b with a and b in C and vertical bar a vertical bar <= 1. We obtain necessary and sufficient conditions for {psi(p)a(n) : n is a non-negative integer} to be a subset of the interior of the numerical range of C-psi,C-phi, where p is the fixed point of phi. We characterize when 0 belongs to the numerical range of a weighted composition operator and determine which weighted composition operators have numerical ranges with no corner points. Furthermore, we describe the corner points of the closure of the numerical range of a compact weighted composition operator. Moreover, we precisely determine the numerical range of C-psi,C-phi when vertical bar a vertical bar = 1.

引用

页码：1529 / 1541

页数：13

共 24 条

[1] The numerical range of a composition operator with conformal automorphism symbol [J].