The Bohr-Favard inequalities for operators
The problem under consideration is to estimate the value \(\|A^{-1}\|\) for the generator \(iA\) of an arbitrary isometric group of operators \(T:{\mathbb R} \to \text{End}X\) under the assumption \(0\in\mathbb{C}\setminus \sigma(A)\). One of the main results of the paper is that, if \(\sigma(A)\subset [\alpha,\infty)\), where \(\alpha>0\) and \(\alpha\in\sigma(A)\), then \(\|A^{-1}\|=r(A^{-1})=1/\alpha\), where \(r(A^{-1})\) is the spectral radius of the operator \(A^{-1}\).
scientific article; zbMATH DE number 5655839