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

^*Korresponderande författare för detta arbete

Forskningsoutput: Tidskriftsbidrag › Artikel › Vetenskaplig › Peer review

10 Citeringar (Scopus)

Sammanfattning

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.

Originalspråk	Engelska
Sidor (från-till)	75-86
Antal sidor	12
Tidskrift	Integral Equations and Operator Theory
Volym	53
Nummer	1
DOI	https://doi.org/10.1007/s00020-004-1307-7
Status	Publicerad - sep. 2005
MoE-publikationstyp	A1 Tidskriftsartikel-refererad

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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

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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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JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 1

ER -

Spectra of composition operators on BMOA

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