Unbounded Generalization of the Baker–Campbell–Hausdorff Formulae
Abstract
ABSTRACT Based on the operator representation on the module over a Banach algebra, the Baker–Campbell–Hausdorff formula is generalized to be applicable to unbounded infinitesimal generators in Banach spaces. For this purpose, it is necessary to extract a bounded component from a given generally unbounded infinitesimal generator. In this paper, much attention is paid to clarifying the unknown relation between the commutator product and the logarithm of operators. In conclusion, by means of the logarithmic representation of generally unbounded operators, the Baker–Campbell–Hausdorff formula is generalized. As an application, a logarithmic form of the von Neumann equation is presented in which the role of the logarithm as the commutator is clearly seen.
Fields of Study & Subjects
Advanced Topics in Algebra
Advanced Numerical Analysis Techniques
Advanced Algebra and Logic
Publication details
- Journal / source
- Mathematical Methods in the Applied Sciences
- Publisher
- Wiley
- Volume
- 49
- Issue
- 12
- Pages
- 12989–13000
- Publication date
- 8 April 2026
- Language
- EN