Trotter Product Formula for Nonself-adjoint Gibbs Semigroups
نویسنده
چکیده
We prove the trace-norm convergence of the Trotter product formula for nonself-adjoint Gibbs semigroups. For any m-sectorial generators A and B such that e ?tRe 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.
منابع مشابه
Comments on the Trotter Product Formula Error-bound Estimates for Nonself-adjoint Semigroups
Let A be a positive self-adjoint operator and let B be an m-accretive operator which is A-small with a relative bound less than one. Let H = A + B, then H is well-deened on dom(H) = dom(A) and m-accretive. If B is a strictly m-accretive operator obeying dom((H)) dom(A) \ dom((B)) 6 = f0g for some 2 (0; 1]; (1) then for the Trotter product formula we prove that ?
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