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The paper is devoted to evolution equations of the form $\partial$$\partial$t u(t) = --(A + B(t))u(t), t $\in$ I = [0, T ], on separable Hilbertspaces where A is a non-negative self-adjoint operator and B($\times$) isfamily of non-negative self-adjoint operators such that dom(A $\alpha$)$\subseteq$ dom(B(t)) for some $\alpha$ $\in$ [0, 1) and the map A --$\alpha$B($\times$)A --$\alpha$ is H{\"o}lder continuous with the H{\"o}lder exponent$\beta$ $\in$ (0, 1). It is shown that the solution operator U(t, s) of theevolution equation can be approximated in the operator norm by a combination ofsemigroups generated by A and B(t) provided the condition $\beta$ > 2$\alpha$-- 1 is satisfied. The convergence rate for the approximation is given by theH{\"o}lder exponent $\beta$. The result is proved using the evolution semigroupapproach.

Trotter product formula and linear evolution equations on Hilbert spaces On the occasion of the 100th birthday of Tosio Kato