Essential Norms of difference of generalized composition Operators from $α$-Bloch spaces to $β$-Bloch spaces

Abstract: In this paper, we study the boundedness and essential norms of the differences of two generalized composition operators acting from $\alpha$-Bloch space to $\beta$-Bloch space on the open unit disk. From essential norms, we get the compactness of the differences of two generalized composition operators. This study has a relationship to the topological structure of generalized composition operators acting from $\alpha$-Bloch space to $\beta$-Bloch space.