Unbounded generalization of the Baker-Campbell-Hausdorff formulae

Abstract

Based on the operator representation on the module over Banach algebra $B(X)$, the Campbell-Baker-Hausdorff formula is generalized to the unbounded situations. In conclusion, by means of the logarithmic representation of generally-unbounded operators, the Campbell-Baker-Hausdorff formula is generalized to be applicable to the unbounded operators.