 00114 Cachia V., Neidhardt H., Zagrebnov V.A.
 Accretive perturbations and error estimates for the Trotter product formula
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Mar 15, 00

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Abstract. We study the error bound estimate in the operatornorm topology for the
exponential Trotter product formula in the case of accretive
perturbations. Let $A$ be a semibounded from below selfadjoint operator on a
separable Hilbert space. Let $B$ be a closed maximal accretive operator which
is, together with $B^*$, Katosmall with respect to $A$ with relative bounds
less than one. We show that in this case the operatornorm error bound estimate
for the exponential Trotter product formula is the same as for the selfadjoint
$B$ \cite{NZ1}:
$$\left\\left(e^{tA/n}e^{tB/n}\right)^n  e^{t(A+B)}\right\ \leq L {\ln
n\over n},\ n = 2,3,\ldots\,.$$
We verify that the operator $(A+B)$ generates a holomorphic contraction
semigroup. One gets a similar result when $B$ is substituted by $B^*$.
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