Gallardo Gutiérrez, Eva AntoniaGonzález, María J.2023-06-202023-06-202003Gallardo Gutiérrez, E. A. & González, M. J. «Exceptional Sets and Hilbert–Schmidt Composition Operators». Journal of Functional Analysis, vol. 199, n.o 2, abril de 2003, pp. 287-300. DOI.org (Crossref), https://doi.org/10.1016/S0022-1236(02)00006-X.0022-123610.1016/S0022-1236(02)00006-Xhttps://hdl.handle.net/20.500.14352/58436It is shown that an analytic map phi of the unit disk into itself inducing a Hilbert-Schmidt composition operator on the Dirichlet space has the property that the set E-phi = {e(i0)is an element ofpartial derivativeD : \phi(e(10))\ = 1 has zero logarithmic capacity. We also show that this is no longer true for compact composition operators on the Dirichlet space. Moreover, such a condition is not even satisfied by Hilbert-Schmidt composition operators on the Hardy space.engjournal articlehttps//doi.org/10.1016/S0022-1236(02)00006-Xhttp://www.sciencedirect.com/science/article/pii/S002212360200006Xrestricted access517Hilbert-Schmidt operatorComposition operatorDirichlet spaceLogarithmic capacityAnálisis matemático1202 Análisis y Análisis Funcional