Choa, Jun Soo; Kim, Hong Oh; Shapiro, Joel H. Compact composition operators on the Smirnov class. (English) Zbl 0954.47028 Proc. Am. Math. Soc. 128, No. 8, 2297-2308 (2000). The authors show that a composition operator \[ G_{\varphi }f(z)=f(\varphi (z)),z\in D, \] where \(\varphi \) is a holomorphic mapping of the unit disk in \(\mathbb{C}\) is compact on the Smirnov class \(N^{+}\) if and only if it is compact on some (equivalently: every) Hardy space \(H^{p}(D)\) , \(0<p<\infty .\) Reviewer: Vladimir S.Rabinovich (Mexico) Cited in 8 Documents MSC: 47B33 Linear composition operators 47B07 Linear operators defined by compactness properties 47B38 Linear operators on function spaces (general) 30D55 \(H^p\)-classes (MSC2000) 46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces Keywords:composition operator; Smirnov class; Hardy space PDFBibTeX XMLCite \textit{J. S. Choa} et al., Proc. Am. Math. Soc. 128, No. 8, 2297--2308 (2000; Zbl 0954.47028) Full Text: DOI