Multiplicative partial integration and the Trotter Product Formula

Trotter-Kato product formula for unitary groups

Let A and B be non-negative self-adjoint operators in a separable Hilbert space such that its form sum C is densely defined. It is shown that the Trotter product formula holds for imaginary times in the L-norm, that is, one has

A Quantum Stochastic Lie-trotter Product Formula

A Trotter product formula is established for unitary quantum stochastic processes governed by quantum stochastic differential equations with constant bounded coefficients.

On Error Estimates for the Trotter-kato Product Formula

We study the error bound in the operator norm topology for the Trotter exponential product formula as well as for its generalization a la Kato. In the frame of the abstract setting we give a simple proof of error estimates which improve some of recent results in this direction.

The Trotter Product Formula for Perturbations of Semibounded Operators

Trotter Product Formula for Nonself-adjoint Gibbs Semigroups

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.