Let M be a von Neumann algebra and a strongly continuous one-parameter group of ^*-automorphisms of M. Recently, considerable interest has been shown in the associated mappings (see for instance [2], [3] and [4]). The paper of Thaheem, Van Daele and Vanheeswijk [4] exclusively deals with these mappings. The main result of [4] is formulated as follows. Let and be strongly continuous one-parameter groups of _*-automorphisms on a von Neumann algebra M satisfying the operator equation