Convergence estimates for the Magnus expansion IA. Uniformly convex 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 IA, we consider uniform convexity. Notions of uniformly convex algebras are discussed, and uniform convexity is shown to improve convergence estimates.

45 pages