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

Title:

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

Creator:

Fatehi, Mahsa and Robati, Bahram Khani

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:2003dac5-004a-4cfa-92ac-b3d12073fada
uuid:2003dac5-004a-4cfa-92ac-b3d12073fada

Subject:

Hardy spaces, essentially normal, composition operator, and linear-fractional transformation

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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 $F(\varphi )$, $\varphi \in {\cal S}(2)$, 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 $H^{2}$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

901-917

Source:

Czechoslovak Mathematical Journal | 2012 Volume:62 | Number:4

Harvested from:

CDK

Metadata only:

false