We determine the spectra of weighted composition operators acting on the weighted Banach spaces of analytic functions H∞ vp when the symbol φ has a fixed point in the open unit disk. Further, we apply this result to give the spectra of composition operators on Bloch type spaces. In particular, we answer in the affirmative a conjecture by MacCluer and Saxe.

Norm and essential norm of differences of differentiation composition operators between Bloch spaces have been estimated in this paper. As a result, we find characterizations for boundedness and compactness of these operators.