Compact linear combinations of composition operators induced by linear fractional maps

被引：15
|
作者：
Choe, Boo Rim [1 ]
Koo, Hyungwoon [1 ]
Wang, Maofa [2 ]
Yang, Jongho [1 ]
机构：
[1] Korea Univ, Dept Math, Seoul 136713, South Korea
[2] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China
来源：
MATHEMATISCHE ZEITSCHRIFT | 2015年 / 280卷 / 3-4期
关键词：
Linear combination of composition operators; Linear fractional map; Compact operator; Hardy space; Weighted Bergman space; BERGMAN SPACES; UNIT BALL; DIFFERENCE;
D O I：
10.1007/s00209-015-1449-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It has been known that the difference of two composition operators induced by linear fractional self-maps of a ball cannot be nontrivially compact on either the Hardy space or any standard weighted Bergman space. In this paper we extend this result in two significant directions: the difference is extended to general linear combinations and inducing maps are extended to linear fractional maps taking a ball into another possibly of different dimension.
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页码：807 / 824
页数：18
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