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 φ is a linear-fractional self-map of D. In this paper first, we investigate the essential normality problem for the operator T w \({C_\varphi }\) 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.
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Fatehi, M., Robati, B.K. Essential normality for certain finite linear combinations of linear-fractional composition operators on the Hardy space H 2 . Czech Math J 62, 901–917 (2012). https://doi.org/10.1007/s10587-012-0073-y
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DOI: https://doi.org/10.1007/s10587-012-0073-y