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.

引用

页数：11

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