Essential normality for certain finite linear combinations of linear-fractional composition operators on the Hardy space $H^{2}$
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 901-917.

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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 $C_{\varphi }$, 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 $H^{2}$.
DOI : 10.1007/s10587-012-0073-y
Classification : 30H10, 46E20, 47B33, 47B35
Mots-clés : Hardy spaces; essentially normal; composition operator; linear-fractional transformation 
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Fatehi, Mahsa; Robati, Bahram Khani. Essential normality for certain finite linear combinations of linear-fractional composition operators on the Hardy space $H^{2}$. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 901-917. doi : 10.1007/s10587-012-0073-y. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0073-y/

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