Compact differences of composition operators from Bloch space to bounded holomorphic function space in the Polydisc

Details Compact differences of composition operators from Bloch space to bounded holomorphic function space in the Polydisc Compact differences of composition operators from Bloch space to bounded holomorphic function space in the Polydisc

2007-09-10

arxiv.org/abs/0709.1420v1

Mathematics

Functional Analysis

9 pages

Scientific paper

Let $\phi$ and $\psi$ be holomorphic self-maps of the unit polydisc $U^n$ in the $n$-dimensional complex space, and denote by $C_{\phi}$ and $C_{\psi}$ the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators $C_{\phi}-C_{\psi}$ from Bloch space to bounded holomorphic function space in the unit polydisc. Moreover the compactness of the difference is also characterized.

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