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On coefficients of vector-valued Bloch functions
Let $X$ be a complex Banach space and let $\mathop{\rm Bloch}(X)$ denote the space of $X$-valued analytic functions on the unit disc such that $\sup_{|z|<1}(1-|z|^2)\|f'(z)\|<\infty$. A sequence $(T_n)_n$ of bounded operators between two Banach spaces $X$