Closed Range Type Properties of Toeplitz Operators on the Bergman Space and the Berezin Transform

被引：7
|
作者：
Zorboska, Nina [1 ]
机构：
[1] Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada
来源：
COMPLEX ANALYSIS AND OPERATOR THEORY | 2019年 / 13卷 / 08期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Multiplication operator; Toeplitz operator; Bergman space; Berezin transform; Closed range operator; Invertible operator; Fredholm operator; Interpolating Blaschke product; HANKEL-OPERATORS;
D O I：
10.1007/s11785-019-00949-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We characterize the multiplication operators with closed range on the Bergman space in terms of the Berezin transform, and apply this characterization to finite products of interpolating Blaschke products. We give some necessary and some sufficient conditions for invertibility of general Toeplitz operators on the Bergman space. We determine the Fredholm Toeplitz operators with B M O-1 symbols and the invertible Toeplitz operators with nonnegative symbols, when their Berezin transform is bounded and of vanishing oscillation.
引用
收藏
页码：4027 / 4044
页数：18
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