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

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

2010-08-10

arxiv.org/abs/1008.1675v1

Mathematics

Complex Variables

18 pages

Scientific paper

We find a lower bound for the essential norm of the difference of two
composition operators acting on $H^2(B_N)$ or $A^2_s(B_N)$ ($s>-1$). 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.

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