Difference of Composition Operators on Hardy Space

W Al-Rawashdeh, Sivaram Krishnan Narayan

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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
JournalJournal of Mathematical Inequalities
Issue number7
StatePublished - 2013


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