On the Wandering Property in Dirichlet spaces

被引：3
|
作者：
Gallardo-Gutierrez, Eva A. [1 ,2 ]
Partington, Jonathan R. [3 ]
Seco, Daniel [2 ,4 ]
机构：
[1] Univ Complutense Madrid, Fac Matemat, Dept Anal Matemat & Matemat Aplicada, Plaza Ciencias 3, E-28040 Madrid, Spain
[2] Inst Ciencias Matemat CSIC UAM UC3M UCM, Madrid, Spain
[3] Univ Leeds, Sch Math, Leeds LS2 9JT, W Yorkshire, England
[4] Univ Carlos III Madrid, Dept Matemat, Ave Univ 30, Madrid 28911, Spain
来源：
INTEGRAL EQUATIONS AND OPERATOR THEORY | 2020年 / 92卷 / 02期
关键词：
Wandering subspace property; Dirichlet spaces; Shift operators; Blaschke products; Renorming; INVARIANT SUBSPACES; BERGMAN; MULTIPLIERS; OPERATORS;
D O I：
10.1007/s00020-020-2573-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that in a scale of weighted Dirichlet spaces Da, including the Bergman space, given any finite Blaschke product B there exists an equivalent norm in Da such that B satisfies the wandering subspace property with respect to such norm. This extends, in some sense, previous results by Carswell et al. (Indiana Univ Math J 51(4):931-961, 2002). As a particular instance, when B(z) = zk and |a| = log(2) log(k+1), the chosen norm is the usual one in D-alpha.
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页数：11
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