Commuting boundedly decomposable perturbations
\textit{C. Apostol} has proved [Rev. Roum. Math. Pures Appl. 13, 1481-1528 (1968; Zbl 0176.437)] that the perturbation of a decomposable operator by a commuting spectral operator is again decomposable. The author generalizes this result by showing that the sum of a decomposable and a commuting boundedly decomposable operator is also decomposable. An example proves this generalization to be nontrivial.
perturbation of a decomposable operator by a commuting spectral operator
the sum of a decomposable and a commuting boundedly decomposable operator is also decomposable
scientific article; zbMATH DE number 4173700