Title: Bloch-type spaces and extended Cesàro operators in the unit ball of a complex Banach space,
Abstract: Let $\mathbb{B}$ be the unit ball of a complex Banach space $X$. In this
paper, we will generalize the Bloch-type spaces and the little Bloch-type
spaces to the open unit ball $\mathbb{B}$ by using the radial derivative. Next,
we define an extended Cesàro operator $T_{\varphi}$ with holomorphic symbol
$\varphi$ and characterize those $\varphi$ for which $T_{\varphi}$ is bounded
between the Bloch-type spaces and the little Bloch-type spaces. We also
characterize those $\varphi$ for which $T_{\varphi}$ is compact between the
Bloch-type spaces and the little Bloch-type spaces under some additional
assumption on the symbol $\varphi$. When $\mathbb{B}$ is the open unit ball of
a finite dimensional complex Banach space $X$, this additional assumption is
automatically satisfied.