Compact differences of weighted composition operators on weighted banach spaces of analytic functions

Let H_μ^∞ (double-struck D sign) be the weighted Banach space of analytic functions with a topology generated by weighted sup-norm. In the present article, we investigate the analytic mappings φ1*phi;2:double-struck D sign → double-struck D sign and θ π : double-struck D sign → ℂ which characterize the compactness of differences of two weighted composition operators Wφ1,θ -Wφ2,π on the space H_μ^∞ (double-struck D sign) . As a consequence we characterize the compactness of differences of composition operators on weighted Bloch spaces.