Gallardo Gutiérrez, Eva AntoniaGonzález, María J.Nieminen, Pekka J.Saksman, Eero2023-06-202023-06-202008Gallardo Gutiérrez, E. A., et al. «On the Connected Component of Compact Composition Operators on the Hardy Space». Advances in Mathematics, vol. 219, n.o 3, octubre de 2008, pp. 986-1001. DOI.org (Crossref), https://doi.org/10.1016/j.aim.2008.06.005.0001-870810.1016/j.aim.2008.06.005https://hdl.handle.net/20.500.14352/50595We show that there exist non-compact composition operators in the connected component of the compact ones on the classical Hardy space H-2. This answers a question posed by Shapiro and Sundberg in 1990. We also establish an improved version of a theorem of MacCluer, giving a lower bound for the essential norm of a difference of composition operators in terms of the angular derivatives of their symbols. As a main tool we use Aleksandrov-Clark measures.engjournal articlehttps//doi.org/10.1016/j.aim.2008.06.005http://www.sciencedirect.com/science/article/pii/S0001870808001564restricted access517Composition operatorsAleksandrov-Clark measuresCompact operatorAnálisis matemático1202 Análisis y Análisis Funcional