Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (5): 1679-1693.doi: 10.1016/S0252-9602(11)60353-6

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COMPACT DIFFERENCES OF COMPOSITION OPERATORS ON HOLOMORPHIC FUNCTION SPACES IN THE UNIT BALL

 JIANG Liang-Ying, OUYANG Cai-Heng   

  1. Department of Mathematics, Tongji University, Shanghai 200092, China;Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209, China; Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
  • Received:2010-08-16 Online:2011-09-20 Published:2011-09-20

Abstract:

We find a lower bound for the essential norm of the difference of two compo-sition operators acting on H2(BN) or A2s(BN) (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.

Key words: composition operators, Hardy space, Bergman spaces, compact differences

CLC Number: 

  • 47B33
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