| 摘 要： | Let B be the unit ball of a complex Banach space X. In this paper, we generalize the Bloch-type spaces and the little Bloch-type spaces to the open unit ball B by using the radial derivative. Next, we de?ne an extended Ces`aro operator T_φ with the holomorphic symbol φ and characterize those φ for which T_φ is bounded between the Bloch-type spaces and the little Bloch-type spaces. We also characterize those φ for which T_φ is compact between the Bloch-type spaces and the little Bloch-type spaces under some additional assumption on the symbol φ. When B is the open unit ball of a ?nite dimensional complex Banach space X, this additional assumption is automatically satis?ed.
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