Compact and Hilbert-Schmidt Differences of Weighted Composition Operators

被引：12

作者：

Acharyya, Soumyadip ^{[1
]}

Wu, Zhijian ^{[2
]}

机构：

[1] Embry Riddle Aeronaut Univ Worldwide, Dept Math Phys & Life Sci, Daytona Beach, FL 32114 USA

[2] Univ Nevada, Dept Math Sci, Las Vegas, NV 89154 USA

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2017年 / 88卷 / 04期

关键词：

Weighted composition operator; Compactness; Hilbert-Schmidt; Bergman space; Hardy space; BERGMAN SPACES; ESSENTIAL NORM; HARDY;

D O I：

10.1007/s00020-017-2374-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we first obtain a characterization of compact difference of two weighted composition operators acting between the standard weighted Bergman spaces, under certain restrictions on the weights. We also calculate (upto equivalence) the Hilbert-Schmidt norm of a difference of two weighted composition operators acting from a Bergman space or Hardy space to an space. This result is followed by a few corollaries involving certain particular types of weights. We also investigate conditions for two weighted composition operators to lie on the same path component under the Hilbert-Schmidt norm topology.

引用

页码：465 / 482

页数：18

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