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.

The multiplicative perturbation bounds for weighted unitary polar factor are considered in the weighted unitary invariant norm, weighted spectral norm, and weighted Frobenius norm in this paper. As the special cases, new bounds for subunitary and unitary polar factor are also derived. These new bounds improve the corresponding results published recently to some extent. Mathematics subject class...

in this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted dirichlet spaces or bloch type spaces to $q_k$ type spaces.