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

^*Tämän työn vastaava kirjoittaja

Tutkimustuotos: Lehtiartikkeli › Artikkeli › Tieteellinen › vertaisarvioitu

10 Sitaatiot (Scopus)

Abstrakti

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.

Alkuperäiskieli	Englanti
Sivut	75-86
Sivumäärä	12
Julkaisu	Integral Equations and Operator Theory
Vuosikerta	53
Numero	1
DOI - pysyväislinkit	https://doi.org/10.1007/s00020-004-1307-7
Tila	Julkaistu - syysk. 2005
OKM-julkaisutyyppi	A1 Julkaistu artikkeli, soviteltu

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10.1007/s00020-004-1307-7

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title = "Spectra of composition operators on BMOA",

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.",

year = "2005",

month = sep,

doi = "10.1007/s00020-004-1307-7",

language = "English",

volume = "53",

pages = "75--86",

journal = "Integral Equations and Operator Theory",

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TY - JOUR

T1 - Spectra of composition operators on BMOA

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

UR - http://www.scopus.com/inward/record.url?scp=24944499211&partnerID=8YFLogxK

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

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