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Linear combination of composition operators on H^∞ and the Bloch space

2018/02/12 by Shi, Yecheng, Li, Songxiao
#Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1802.04092

Abstract

Let λi (i=1,...,k) be any nonzero complex scalars and φi (i=1,..,k) be any analytic self-maps of the unit disk \mathbbD. We show that the operator ∑i=1kλiCφi is compact on the Bloch space B if and only if limn→∞‖λ1φ1n2φ2n+...+λkφknB=0. We also study the linear combination of composition operators on the Banach algebra of bounded analytic functions.

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