## 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 (W_{w,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(H^{2}), and we find a sufficient condition for the difference of such operators to be compact on H^{2}(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 H^{2}(D{double-struck}).

Original language | English |
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Pages (from-to) | 427-444 |

Journal | Journal of Mathematical Inequalities |

Issue number | 7 |

State | Published - 2013 |