Spectrum

Abstract

Let $T:\mathcal{D}(T)\to\mathcal{X}$ be a linear transformation, where $\mathcal{X}$ is a nonzero normed space and $\mathcal{D}T$, the domain of T, is a linear manifold of $\mathcal{X}$. The general notion of spectrum, which applies to bounded or unbounded transformations, goes as follows.