Spectra of weighted composition operators with automorphic symbols

Olli Hyvärinen; Mikael Lindström; Ilmari Nieminen; Erno Saukko

doi:10.1016/j.jfa.2013.06.003

Spectra of weighted composition operators with automorphic symbols

Olli Hyvärinen
, Mikael Lindström^*
, Ilmari Nieminen
, Erno Saukko

^*Corresponding author for this work

Mathematics

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

48 Citations (Scopus)

Abstract

Let φ be an automorphism of the open unit disc D. For such φ, we investigate the spectra of invertible weighted composition operators uC_φ acting on a wide class of analytic function spaces; this class contains, for example, Hardy spaces Hp(D), weighted Bergman spaces Aαp(D), and weighted Banach spaces of H^∞-type. We present new techniques for deducing the spectrum and for calculating the spectral radius of uC_φ. We also characterize the Fredholmness of weighted composition operators on Hp(D) and Aαp(D).

Original language	English
Pages (from-to)	1749-1777
Number of pages	29
Journal	Journal of Functional Analysis
Volume	265
Issue number	8
DOIs	https://doi.org/10.1016/j.jfa.2013.06.003
Publication status	Published - 15 Oct 2013
MoE publication type	A1 Journal article-refereed

Keywords

Automorphism
Fredholm operator
Hardy spaces
Spectrum
Weighted Banach spaces of H-type
Weighted Bergman spaces
Weighted composition operator

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abstract = "Let φ be an automorphism of the open unit disc D. For such φ, we investigate the spectra of invertible weighted composition operators uCφ acting on a wide class of analytic function spaces; this class contains, for example, Hardy spaces Hp(D), weighted Bergman spaces Aαp(D), and weighted Banach spaces of H∞-type. We present new techniques for deducing the spectrum and for calculating the spectral radius of uCφ. We also characterize the Fredholmness of weighted composition operators on Hp(D) and Aαp(D).",

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T1 - Spectra of weighted composition operators with automorphic symbols

AU - Hyvärinen, Olli

AU - Lindström, Mikael

AU - Nieminen, Ilmari

AU - Saukko, Erno

PY - 2013/10/15

Y1 - 2013/10/15

N2 - Let φ be an automorphism of the open unit disc D. For such φ, we investigate the spectra of invertible weighted composition operators uCφ acting on a wide class of analytic function spaces; this class contains, for example, Hardy spaces Hp(D), weighted Bergman spaces Aαp(D), and weighted Banach spaces of H∞-type. We present new techniques for deducing the spectrum and for calculating the spectral radius of uCφ. We also characterize the Fredholmness of weighted composition operators on Hp(D) and Aαp(D).

AB - Let φ be an automorphism of the open unit disc D. For such φ, we investigate the spectra of invertible weighted composition operators uCφ acting on a wide class of analytic function spaces; this class contains, for example, Hardy spaces Hp(D), weighted Bergman spaces Aαp(D), and weighted Banach spaces of H∞-type. We present new techniques for deducing the spectrum and for calculating the spectral radius of uCφ. We also characterize the Fredholmness of weighted composition operators on Hp(D) and Aαp(D).

KW - Automorphism

KW - Fredholm operator

KW - Hardy spaces

KW - Spectrum

KW - Weighted Banach spaces of H-type

KW - Weighted Bergman spaces

KW - Weighted composition operator

UR - https://www.scopus.com/pages/publications/84880624918

U2 - 10.1016/j.jfa.2013.06.003

DO - 10.1016/j.jfa.2013.06.003

M3 - Article

AN - SCOPUS:84880624918

SN - 0022-1236

VL - 265

SP - 1749

EP - 1777

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 8

ER -

Spectra of weighted composition operators with automorphic symbols

Abstract

Keywords

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