Trotter-Kato product formula for unitary groups

Abstract

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 $L^2$-norm. The result remains true for the Trotter-Kato product formula for so-called holomorphic Kato functions; we also derive a canonical representation for any function of this class.