Spectra of composition operators on BMOA

M. Lindström; N. Palmberg

doi:10.1007/s00020-004-1307-7

Spectra of composition operators on BMOA

M. Lindström^*, N. Palmberg

^*Corresponding author for this work

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

10 Citations (Scopus)

Abstract

It is shown that if φ is a univalent self-map on the unit disk double-struck D sign is not an automorphism and has a fixed point in double-struck D sign and if the essential spectral radius of the composition operator C φ on H ² is different from zero, then the spectrum of C φ on BMOA coincides with double-struck D sign̄. This answers in the affirmative a conjecture by MacCluer and Saxe.

Original language	English
Pages (from-to)	75-86
Number of pages	12
Journal	Integral Equations and Operator Theory
Volume	53
Issue number	1
DOIs	https://doi.org/10.1007/s00020-004-1307-7
Publication status	Published - Sept 2005
MoE publication type	A1 Journal article-refereed

Keywords

BMOA
Essential norm
Essential spectral radius
N
Spectrum
Weighted composition operator

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10.1007/s00020-004-1307-7

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abstract = "It is shown that if φ is a univalent self-map on the unit disk double-struck D sign is not an automorphism and has a fixed point in double-struck D sign and if the essential spectral radius of the composition operator C φ on H 2 is different from zero, then the spectrum of C φ on BMOA coincides with double-struck D sig{\=n}. This answers in the affirmative a conjecture by MacCluer and Saxe.",

keywords = "BMOA, Essential norm, Essential spectral radius, N, Spectrum, Weighted composition operator",

author = "M. Lindstr{\"o}m and N. Palmberg",

note = "Funding Information: The research of the authors was partially supported by the Academy of Finland Project No. 51906; the research of this paper was carried out while these authors were visiting Kent State University, whose hospitality is acknowledged with thanks.",

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AU - Lindström, M.

AU - Palmberg, N.

N1 - Funding Information: The research of the authors was partially supported by the Academy of Finland Project No. 51906; the research of this paper was carried out while these authors were visiting Kent State University, whose hospitality is acknowledged with thanks.

PY - 2005/9

Y1 - 2005/9

N2 - It is shown that if φ is a univalent self-map on the unit disk double-struck D sign is not an automorphism and has a fixed point in double-struck D sign and if the essential spectral radius of the composition operator C φ on H 2 is different from zero, then the spectrum of C φ on BMOA coincides with double-struck D sign̄. This answers in the affirmative a conjecture by MacCluer and Saxe.

AB - It is shown that if φ is a univalent self-map on the unit disk double-struck D sign is not an automorphism and has a fixed point in double-struck D sign and if the essential spectral radius of the composition operator C φ on H 2 is different from zero, then the spectrum of C φ on BMOA coincides with double-struck D sign̄. This answers in the affirmative a conjecture by MacCluer and Saxe.

KW - BMOA

KW - Essential norm

KW - Essential spectral radius

KW - N

KW - Spectrum

KW - Weighted composition operator

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U2 - 10.1007/s00020-004-1307-7

DO - 10.1007/s00020-004-1307-7

M3 - Article

AN - SCOPUS:24944499211

SN - 0378-620X

VL - 53

SP - 75

EP - 86

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 1

ER -

Spectra of composition operators on BMOA

Abstract

Keywords

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