Let $X$ be a [Banach space](/page/Banach%20Space), let $I:X\to X$ denote the identity operator, let $B\in\mathcal{L}(X)$ be an invertible [bounded linear operator](/page/Bounded%20Linear%20Operator) with inverse $B^{-1}\in\mathcal{L}(X)$, and let $E\in\mathcal{L}(X)$ be a bounded linear operator. If