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oai:docta.ucm.es:20.500.14352/584362024-07-12T14:21:23Zcom_20.500.14352_14col_20.500.14352_15

Exceptional sets and Hilbert–Schmidt composition operators Gallardo Gutiérrez, Eva Antonia González, María J. It 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. 2023-06-20T18:43:28Z 2023-06-20T18:43:28Z 2023-06-20T18:43:28Z 2003 journal article https://hdl.handle.net/20.500.14352/58436 0022-1236 10.1016/S0022-1236(02)00006-X eng BFM2000-0360 FQM-260 PB98-0872 1998SRG00052 Gallardo 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. restricted access Elsevier