Compact Differences of Composition Operators on Holomorphic Function Spaces in the Unit Ball

Liangying Jiang; Caiheng Ouyang

paper

Compact Differences of Composition Operators on Holomorphic Function Spaces in the Unit Ball

arXiv:1008.1675

Abstract

We find a lower bound for the essential norm of the difference of two composition operators acting on $H^{2} (B_{N})$ or $A_{s}^{2} (B_{N})$ ( $s > - 1$ ). This result plays an important role in proving a necessary and sufficient condition for the difference of linear fractional composition operators to be compact, which answers a question posed by MacCluer and Weir in 2005.

18 pages