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We study the boundedness and compactness of the differences of two weighted composition operators acting from the Bloch space B to the space H∞ of bounded analytic functions on the open unit disk. Such a study has a relationship to the topological structure problem of composition operators on H∞. Using this relation, we will estimate the operator norms and the essential norms of the differences of two composition operators acting from B to H∞.

Differences of weighted composition operators acting from Bloch space to 𝐻^{∞}