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

2010/08/10 by Liangying Jiang, Jiang, Liangying, Caiheng Ouyang +1
Mathematics · #32A35 (Secondary) #32A36 #47B38 (Primary) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #math.CV #math.FA #msc:32A35 #msc:32A36 #msc:47B38

paper · pdf · doi:10.48550/arxiv.1008.1675

18 pages

arxiv created 2010/08/10 · arxiv updated 2010/08/11

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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