Wolf, Elke Differences of composition operators between weighted Banach spaces of holomorphic functions on the unit polydisk. (English) Zbl 1154.47018 Result. Math. 51, No. 3-4, 361-372 (2008). By introducing an auxiliary associated weight, the author gives an estimate in terms of pseudohyperbolic distance for the essential norm of the difference of composition operators between given weighted Banach spaces \(H_v^\infty\) or \(H_v^0\) of holomorphic functions on the unit polydisk. This result can lead to conditions for the differences to be compact. Reviewer: Pengyan Hu (Shenzhen) Cited in 8 Documents MSC: 47B33 Linear composition operators 47B38 Linear operators on function spaces (general) 32A10 Holomorphic functions of several complex variables 47B39 Linear difference operators Keywords:unit polydisk; compact operator; essential norm; differences of composition operators; weighted Banach spaces of holomorphic functions PDFBibTeX XMLCite \textit{E. Wolf}, Result. Math. 51, No. 3--4, 361--372 (2008; Zbl 1154.47018) Full Text: DOI