Essential normality for certain finite linear combinations of linear-fractional composition operators on the Hardy space H 2

Mahsa Fatehi; Bahram Khani Robati

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 4, page 901-917
  • ISSN: 0011-4642

Abstract

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In 1999 Nina Zorboska and in 2003 P. S. Bourdon, D. Levi, S. K. Narayan and J. H. Shapiro investigated the essentially normal composition operator C ϕ , when ϕ is a linear-fractional self-map of 𝔻 . In this paper first, we investigate the essential normality problem for the operator T w C ϕ on the Hardy space H 2 , where w is a bounded measurable function on ∂ 𝔻 which is continuous at each point of F ( ϕ ) , ϕ ∈ 𝒮 ( 2 ) , and T w is the Toeplitz operator with symbol w . Then we use these results and characterize the essentially normal finite linear combinations of certain linear-fractional composition operators on H 2 .

How to cite

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Fatehi, Mahsa, and Robati, Bahram Khani. "Essential normality for certain finite linear combinations of linear-fractional composition operators on the Hardy space $H^{2}$." Czechoslovak Mathematical Journal 62.4 (2012): 901-917. <http://eudml.org/doc/246398>.

@article{Fatehi2012,
abstract = {In 1999 Nina Zorboska and in 2003 P. S. Bourdon, D. Levi, S. K. Narayan and J. H. Shapiro investigated the essentially normal composition operator $C_\{\varphi \}$, when $\varphi $ is a linear-fractional self-map of $\mathbb \{D\}$. In this paper first, we investigate the essential normality problem for the operator $T_\{w\}C_\{\varphi \}$ on the Hardy space $H^\{2\}$, where $w$ is a bounded measurable function on $\partial \mathbb \{D\}$ which is continuous at each point of $F(\varphi )$, $\varphi \in \{\mathcal \{S\}\}(2)$, and $T_\{w\}$ is the Toeplitz operator with symbol $w$. Then we use these results and characterize the essentially normal finite linear combinations of certain linear-fractional composition operators on $H^\{2\}$.},
author = {Fatehi, Mahsa, Robati, Bahram Khani},
journal = {Czechoslovak Mathematical Journal},
keywords = {Hardy spaces; essentially normal; composition operator; linear-fractional transformation; Hardy space; essentially normal composition operator; linear-fractional transformation},
language = {eng},
number = {4},
pages = {901-917},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Essential normality for certain finite linear combinations of linear-fractional composition operators on the Hardy space $H^\{2\}$},
url = {http://eudml.org/doc/246398},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Fatehi, Mahsa
AU - Robati, Bahram Khani
TI - Essential normality for certain finite linear combinations of linear-fractional composition operators on the Hardy space $H^{2}$
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 4
SP - 901
EP - 917
AB - In 1999 Nina Zorboska and in 2003 P. S. Bourdon, D. Levi, S. K. Narayan and J. H. Shapiro investigated the essentially normal composition operator $C_{\varphi }$, when $\varphi $ is a linear-fractional self-map of $\mathbb {D}$. In this paper first, we investigate the essential normality problem for the operator $T_{w}C_{\varphi }$ on the Hardy space $H^{2}$, where $w$ is a bounded measurable function on $\partial \mathbb {D}$ which is continuous at each point of $F(\varphi )$, $\varphi \in {\mathcal {S}}(2)$, and $T_{w}$ is the Toeplitz operator with symbol $w$. Then we use these results and characterize the essentially normal finite linear combinations of certain linear-fractional composition operators on $H^{2}$.
LA - eng
KW - Hardy spaces; essentially normal; composition operator; linear-fractional transformation; Hardy space; essentially normal composition operator; linear-fractional transformation
UR - http://eudml.org/doc/246398
ER -

References

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