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

Fatehi, Mahsa ; Robati, Bahram Khani

Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 901-917.

Résumé

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 $C_{\phi }$, when $\phi$ is a linear-fractional self-map of $\mathbb{D}$. In this paper first, we investigate the essential normality problem for the operator $T_w{C}_{\phi }$ on the Hardy space $H^2$, where $w$ is a bounded measurable function on $\partial \mathbb{D}$ which is continuous at each point of $F(\phi )$, $\phi \in \mathcal{S}(2)$, 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 $H^2$.

Détail

DOI : 10.1007/s10587-012-0073-y

Classification : 30H10, 46E20, 47B33, 47B35
Mots-clés : Hardy spaces; essentially normal; composition operator; linear-fractional transformation