Convergence estimates for the Magnus expansion II. $C^*$-algebras

Abstract

We review and provide simplified proofs related to the Magnus expansion, and improve convergence estimates. Observations and improvements concerning the Baker--Campbell--Hausdorff expansion are also made. In this Part II, we prove growth estimates regarding the Magnus expansion in the setting Hilbert space operators near the critical cumulative norm $\pi$. We also conduct a detailed geometrical study in the case of $2\times2$ real matrices, leading to some special normal forms via the Magnus expansion.Comment: Part II of original submission arXiv:1709.01791v1, basically unrewritte