Let \(X\) be an infinite-dimensional complex Banach space, and let \(T\) be a bounded linear operator defined on \(X\) satisfying \(\dim T^{- 1}(0)= 0\), \(\dim X/T(X)= 1\) and \(\bigcap^\infty_{n= 1}T^n(X)= \{0\}\). Such an operator is known as a shift [\textit{R. M. Crownover}, Mich. Math. J. 19, 233-247 (1972; Zbl 0228.47016)]. If \(x_0\) is a fixed norm one vector in \(X\) such that \(X= \text{sp}\{x_0\}+ T(X)\), then each \(x\in X\) has a Taylor polynomial \(x= \sum^n_{k= 0}\alpha_k(x) T^kx_0+ T^{n+ 1}x_{n+ 1}\) \((n\geq 0)\), where the sequences \((\alpha_n(x))^\infty_{n= 0}\) and \((x_n)^\infty_{n= 0}\) are uniquely determined. The sequence space \(X_s= \{(\alpha_n(x))^\infty_{n= 0}:x\in X\}\) with the norm \(\|(\alpha_n(x))^\infty_{n= 0}\|= \| x\|\) is isometrically isomorphic to \(X\), and \(T\) corresponds to the unilateral shift operator \(T_s: X_s\to X_s\) given by \(T_s(\alpha_0,\alpha_1,\alpha_2,\dots)= (0,\alpha_0, \alpha_1,\dots)\). In the paper under review, the author studies perturbations of the form \(T-\lambda I\), properties of the Taylors series \(\sum^\infty_{n= 0}\alpha_n(x)\lambda^n\), orthogonal decompositions, and local spectra of shift isometries; for example, for a shift isometry \(T\), it is shown that the open unit disk coincides with the connected component of the Fredholm resolvent of \(T\) that contains 0, while the closed unit disk coincides with the local spectrum of \(T\) at each \(x\neq 0\).