The essential norm of a composition operator on the minimal Mobius invariant space

Details The essential norm of a composition operator on the minimal Mobius invariant space The essential norm of a composition operator on the minimal Mobius invariant space

2010-05-26

arxiv.org/abs/1005.4935v2

Mathematics

Complex Variables

11 pages

Scientific paper

We derive a formula for the essential norm of a composition operator on the minimal Mobius invariant space of analytic functions. As an application, we show that the essential norm of a non-compact composition operator is at least 1. We also obtain lower bounds depending on the behavior of the symbol near the boundary, and calculate the order of magnitude of the essential norm of composition operators induced by finite Blaschke products.

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