On the connected component of compact composition operators on the Hardy space

• Autores: Eva Antonia Gallardo Gutiérrez , María José González Fuentes , Pekka Nieminen, Eero Saksman
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 219, Nº 3, 2008, págs. 986-1001
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.06.005
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• Resumen

  • We show that there exist non-compact composition operators in the connected component of the compact ones on the classical Hardy space H2. 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.