Cachia, Vincent; Zagrebnov, Valentin A. Trotter product formula for nonself-adjoint Gibbs semigroups. (English) Zbl 1028.47033 J. Lond. Math. Soc., II. Ser. 64, No. 2, 436-444 (2001). 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. Cited in 5 Documents 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 Keywords:trace-norm convergence; Trotter product formula; nonself-adjoint Gibbs semigroups; error bound estimates PDFBibTeX XMLCite \textit{V. Cachia} and \textit{V. A. Zagrebnov}, J. Lond. Math. Soc., II. Ser. 64, No. 2, 436--444 (2001; Zbl 1028.47033) Full Text: DOI