Comments on the Trotter product formula error-bound estimates for non-selfadjoint semigroups (Q1600105)

Let \(A\) be a positive selfadjoint operator in a separable Hilbert space. Let \(B\) be an \(m\)-accretive operator which is relatively bounded with respect to \(A\) with bound less than one. Then \(H=A+B\) is \(m\)-accretive. If \(B\) is strictly \(m\)-accretive and \(D((H^\ast)^\alpha)\subset D(A^\alpha)\cap D((B^\ast)^\alpha)\not=\{0\}\) for some \(\alpha\in (0,1]\), then \(\| (e^{-tB/n}e^{-tA/n})^n-e^{-tH}\| =O(\ln n/n^\alpha)\) as \(n\rightarrow \infty\), uniformly in \(t\geq 0\).