Let ϕ be a linear fractional self-map of the ball BN with a boundary fixed point e1, we show thatholds in a neighborhood of e1 on BN . Applying this result we give a positive answer for a conjecture by MacCluer and Weir, and improve their results relating to the essential normality of composition operators on H 2 (BN ) and A 2 γ (BN ) (γ > −1). Combining this with other related results in MacCluer & Weir, Integral Equations Operator Theory, 2005, we characterize the essential normality of composition operators induced by parabolic or hyperbolic linear fractional self-maps of B2. Some of them indicate a difference between one variable and several variables.
We characterize the spectra of composition operators on the Hardy space H 2 (B N ), when the symbols are elliptic or hyperbolic linear fractional self-maps of B N . Therefore, combining with the result obtained by Bayart [4], the spectra of all linear fractional composition operators on H 2 (B N ) are completely determined.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.