Difference of composition operators on hardy space

Waleed Al-Rawashdeh, Sivaram K. Narayan

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Suppose φ is an analytic self-map of open unit disk D{double-struck} and w is an analytic function on D{double-struck}. Then a weighted composition operator induced by φ with weight w is given by (Ww,φ f)(z) = w(z) f (φ(z)), for z ∈ D{double-struck} and f analytic on D{double-struck}. We find a sufficient condition under which two composition operators lie in the same path component of C(H2), and we find a sufficient condition for the difference of such operators to be compact on H2(D{double-struck}). Then we provide another example that answers a question raised by Shapiro and Sundberg [18] negatively. Moreover, we characterize the Hilbert-Schmidt difference of two composition operators on H2(D{double-struck}).

Original languageEnglish
Pages (from-to)427-444
Number of pages18
JournalJournal of Mathematical Inequalities
Volume7
Issue number3
DOIs
StatePublished - 2013

Keywords

  • Bergman spaces
  • Carleson-type measure
  • Compact operator
  • Hardy space
  • Hilbert-Schmidt operator
  • Pseudo-hyperbolic distance
  • Weighted Composition Operators

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