Note on a product formula for unitary groups

For any nonnegative self-adjoint operators A and B in a separable Hilbert space, we show that the Trotter-type formula $[(e^{i2tA\mathrm{/}n}+e^{i2tB\mathrm{/}n})\mathrm{/}2{]}^n$ converges strongly in the closure of the intersection of the domains of A^{1/2} and B^{1/2}, along some subsequence and for almost every real number t. This result extends to the degenerate case and to Kato-functions following the method of Kato.