The Essential Norm of Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions

Olli Hyvärinen; Mika Kemppainen; Mikael Lindström; Antti Rautio; Erno Saukko

doi:10.1007/s00020-011-1919-7

The Essential Norm of Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions

Olli Hyvärinen^*, Mika Kemppainen, Mikael Lindström, Antti Rautio, Erno Saukko

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › Scientific › peer-review

74 Citations (Scopus)

Abstract

For a wide class of radial weights we calculate the essential norm of a weighted composition operator uCφ on the weighted Banach spaces of analytic functions in terms of the analytic function u:D → ℂ and the nth power of the analytic selfmap φ of the open unit disc D. We also apply our result to calculate the essential norm of composition operators acting on Bloch type spaces with general radial weights.

Original language	English
Pages (from-to)	151-157
Number of pages	7
Journal	Integral Equations and Operator Theory
Volume	72
Issue number	2
DOIs	https://doi.org/10.1007/s00020-011-1919-7
Publication status	Published - Feb 2012
MoE publication type	A1 Journal article-refereed

Keywords

Essential norm
weighted composition operator

Access to Document

10.1007/s00020-011-1919-7

Cite this

@article{aa29d76139ed49c4a01b9bd407c25ef0,

title = "The Essential Norm of Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions",

abstract = "For a wide class of radial weights we calculate the essential norm of a weighted composition operator uCφ on the weighted Banach spaces of analytic functions in terms of the analytic function u:D → ℂ and the nth power of the analytic selfmap φ of the open unit disc D. We also apply our result to calculate the essential norm of composition operators acting on Bloch type spaces with general radial weights.",

keywords = "Essential norm, weighted composition operator",

author = "Olli Hyv{\"a}rinen and Mika Kemppainen and Mikael Lindstr{\"o}m and Antti Rautio and Erno Saukko",

year = "2012",

month = feb,

doi = "10.1007/s00020-011-1919-7",

language = "English",

volume = "72",

pages = "151--157",

journal = "Integral Equations and Operator Theory",

issn = "0378-620X",

publisher = "Springer",

number = "2",

}

TY - JOUR

T1 - The Essential Norm of Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions

AU - Hyvärinen, Olli

AU - Kemppainen, Mika

AU - Lindström, Mikael

AU - Rautio, Antti

AU - Saukko, Erno

PY - 2012/2

Y1 - 2012/2

N2 - For a wide class of radial weights we calculate the essential norm of a weighted composition operator uCφ on the weighted Banach spaces of analytic functions in terms of the analytic function u:D → ℂ and the nth power of the analytic selfmap φ of the open unit disc D. We also apply our result to calculate the essential norm of composition operators acting on Bloch type spaces with general radial weights.

AB - For a wide class of radial weights we calculate the essential norm of a weighted composition operator uCφ on the weighted Banach spaces of analytic functions in terms of the analytic function u:D → ℂ and the nth power of the analytic selfmap φ of the open unit disc D. We also apply our result to calculate the essential norm of composition operators acting on Bloch type spaces with general radial weights.

KW - Essential norm

KW - weighted composition operator

UR - https://www.scopus.com/pages/publications/84855689074

U2 - 10.1007/s00020-011-1919-7

DO - 10.1007/s00020-011-1919-7

M3 - Article

AN - SCOPUS:84855689074

SN - 0378-620X

VL - 72

SP - 151

EP - 157

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 2

ER -

The Essential Norm of Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this