# 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

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topFatehi, 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 -

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