Exponentials of Sums of Operators in a Banach Space

Abstract

Let A and B be bounded linear operators in a Banach space. We consider the following problem: if ∞ 0 e At e Bt dt < ∞, under what conditions we have ∞ 0 e (A+B)t dt < ∞? Our main result is formulated in terms of the norm of the commutator AB − BA.