Bulletin of the Australian Mathematical Society

Research Article

COMPACT DIFFERENCES OF COMPOSITION OPERATORS

ELKE WOLFa1

a1 Mathematical Institute, University of Paderborn, D-33095 Paderborn, Germany (email: lichte@math.uni-paderborn.de)

Abstract

Let xs03D5 and ψ be analytic self-maps of the open unit disk. Each of them induces a composition operator, Cxs03D5 and Cψ respectively, acting between weighted Bergman spaces of infinite order. We show that the difference Cxs03D5Cψ is compact if and only if both operators are compact or both operators are not compact and the pseudohyperbolic distance of the functions xs03D5 and ψ tends to zero if ∣xs03D5(z)∣→1 or ∣ψ(z)∣→1.

(Received June 07 2007)

2000 Mathematics subject classification

  • 47B33;
  • 47B38

Keywords and phrases

  • differences of weighted composition operators;
  • compact;
  • weighted Bergman spaces of infinite order