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

2007/06/18 by Gallardo-Gutiérrez, Eva A., González, Maria J., Nieminen, Pekka +1
#30D55 #47B33 (Primary) #47B38 (Secondary) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.0706.2664

Abstract

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

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