POWERS OF COMPOSITION OPERATORS: ASYMPTOTIC BEHAVIOUR ON BERGMAN, DIRICHLET AND BLOCH SPACES

被引：13

作者：

Arendt, W. ^{[1
]}

Chalendar, I ^{[2
]}

Kumar, M. ^{[3
]}

Srivastava, S. ^{[4
]}

机构：

[1] Univ Ulm, Inst Appl Anal, D-89069 Ulm, Germany

[2] Univ Paris Est, LAMA UMR 8050, UPEM, CNRS,UPEC, F-77454 Marne La Vallee, France

[3] Univ Delhi, Lady Shri Ram Coll Women, Dept Math, Delhi, India

[4] Univ Delhi, Dept Math, South Campus, Delhi, India

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2020年 / 108卷 / 03期

关键词：

composition operators; weighted Bergman spaces; Bloch space; asymptotic behaviour; holomorphic semiflows; WEIGHTED COMPOSITION OPERATORS; BANACH-SPACES; ESSENTIAL NORM; ISOMETRIES; SPECTRA;

D O I：

10.1017/S1446788719000235

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the asymptotic behaviour of the powers of a composition operator on various Banach spaces of holomorphic functions on the disc, namely, standard weighted Bergman spaces (finite and infinite order), Bloch space, little Bloch space, Bloch-type space and Dirichlet space. Moreover, we give a complete characterization of those composition operators that are similar to an isometry on these various Banach spaces. We conclude by studying the asymptotic behaviour of semigroups of composition operators on these various Banach spaces.

引用

页码：289 / 320

页数：32

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