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Bulletin of the Iranian Mathematical Society

, Volume 45, Issue 5, pp 1389–1406 | Cite as

Weighted Space and Bloch-Type Space on the Unit Ball of an Infinite Dimensional Complex Banach Space

  • Zhenhan Tu
  • Liangpeng XiongEmail author
Original Paper
  • 101 Downloads

Abstract

Let \({\mathbf {B}}_{{\mathbb {X}}}\) be the open unit ball of a complex Banach space \({\mathbb {X}}\), which may beinfinite dimensional. The weighted composition operator and weighted space defined on \({\mathbf {B}}_{{\mathbb {X}}}\) are introduced. We obtain the boundedness and compactness of the weightedcomposition operator from the Bloch-type spaces to the weighted spaces, and some properties with the Bloch-type spaces are given. Our main results generalize theprevious works on the Euclidean unit ball \({\mathbb {B}}^n\) to the case of \({\mathbf {B}}_{{\mathbb {X}}}\).

Keywords

Boundedness Complex Banach space Compactness Weighted composition operator Weighted Bloch-type space 

Mathematics Subject Classification

47B38 32A37 46B15 

Notes

Acknowledgements

The project is supported by the National Natural Science Foundation of China (no. 11671306).

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Copyright information

© Iranian Mathematical Society 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanPeople’s Republic of China

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