Continuity of the sequential product of sequential quantum effect algebras

In order to study quantum measurement theory, sequential product defined by A circle B = A(1/2)BA(1/2) for any two quantum effects A, B has been introduced. Physically motivated conditions ask the sequential product to be continuous with respect to the strong operator topology. In this paper, we study the continuity problems of the sequential product A circle B = A(1/2)BA(1/2) with respect to other important topologies, such as norm topology, weak operator topology, order topology, and interval topology. (C) 2016 AIP Publishing LLC.