Let $T\in {\mathcal{L}}(X)$ be a bounded operator on a complex Banach space $X$. If $V$ is an open subset of the complex plane such that $\lambda -T$ is of Kato-type for each $\lambda \in V$, then the induced mapping $f(z)\mapsto (z-T)f(z)$ has closed range in the Fréchet space of analytic $X$-valued functions on $V$. Since semi-Fredholm operators are of Kato-type, this generalizes a result of Eschmeier on Fredholm operators and leads to a sharper estimate of Nagy’s spectral residuum of $T$. Our proof is elementary; in particular, we avoid the sheaf model of Eschmeier and Putinar and the theory of coherent analytic sheaves.