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

Published 10 Aug 2010 in math.CV and math.FA | (1008.1675v1)

Abstract: We find a lower bound for the essential norm of the difference of two composition operators acting on $H2(B_N)$ or $A2_s(B_N)$ ($s>-1$). 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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