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

Liangying Jiang; Caiheng Ouyang

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

Complex Variables 2010-08-11 v1 Functional Analysis

Authors: Liangying Jiang , Caiheng Ouyang

Abstract

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

Keywords

composition operators operator theory pseudodifferential operators

Cite

@article{arxiv.1008.1675,
  title  = {Compact Differences of Composition Operators on Holomorphic Function Spaces in the Unit Ball},
  author = {Liangying Jiang and Caiheng Ouyang},
  journal= {arXiv preprint arXiv:1008.1675},
  year   = {2010}
}

Comments

18 pages

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