Volume 33 • Number 3 • 2010   • The Essential Norm and Spectrum of a Weighted Composition Operator on H∞(BN) Cheng Yuan and Ze-Hua Zhou Abstract. For φ a holomorphic self-map of the unit ball BN of ℂN, and u ∈ H∞(BN) (the Banach space of bounded holomorphic functions on BN), we investigate the essential norm and spectrum of the weighted composition operator uCφ acting on the space H∞(BN). For φ univalent, not unitary on any slice, and fixing a point of BN, we obtain a complete characterization of the spectrum of uCφ. 2010 Mathematics Subject Classification: Primary: 47B38; Secondary: 46E15, 32A37. Full text: PDF