## Differences of composition operators on the Bloch space in the polydisc.(English)Zbl 1166.47032

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

### MSC:

 47B38 Linear operators on function spaces (general) 47B33 Linear composition operators
Full Text:

### References:

 [1] DOI: 10.1016/j.jmaa.2005.04.080 · Zbl 1087.47029 [2] DOI: 10.1007/s00020-002-1203-y · Zbl 1065.47027 [3] Hosokawa, J. Operator. Theory 57 pp 229– (2007) [4] Timoney, J. Reine Angew. Math. 319 pp 1– (1980) · Zbl 0425.32008 [5] DOI: 10.1112/blms/12.4.241 · Zbl 0416.32010 [6] DOI: 10.1007/s00020-002-1180-1 · Zbl 1054.47021
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.