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Trotter product formula for nonself-adjoint Gibbs semigroups. (English) Zbl 1028.47033

Summary: The trace-norm convergence of the Trotter product formula is proved for nonself-adjoint Gibbs semigroups. For any \(m\)-sectorial generators \(A\) and \(B\) such that \(e^{-t \text{Re} A}\) is in the trace-class for \(t>0\), the Trotter product formula converges in the trace-norm. With smallness conditions on \(B\) with respect to \(A\), we give error bound estimates of the convergence rate in this topology.

MSC:

47D06 One-parameter semigroups and linear evolution equations
41A80 Remainders in approximation formulas
47A55 Perturbation theory of linear operators
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
47B44 Linear accretive operators, dissipative operators, etc.
35Q40 PDEs in connection with quantum mechanics
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