Operation Continuity Of Sequential Effect Algebras

The sequential effect algebra is an important model for studying quantum measure-ment theory. A sequential effect algebra is an effect algebra which has a sequential prod-uct operation. In this paper, we study the continuity of sequential product with respect tosome topology on sequential effect algebras.Hilbert space sequential effect algebra ε（H） is one of important sequential effectalgebras. Standard sequential product plays an important role in studying quantum mea-surement theory. It has a sequential product AB=A^1/2BA^2/1 called standard sequentialproduct. In this paper, we mainly study the continuity of the standard sequential producton ε（H） with respect to operator norm topology, strong operator topology, weak operatortopology, order topology and interval topology and that in terms of order convergence.We show that:（1） the standard sequential product is continuous with respect to operatornorm topology and strong operator topology.（2） the standard sequential product is contin-uous with the second variable with respect to weak operator topology, order topology andinterval topology.（3） the standard sequential product is order continuous with the secondvariable. We give examples to show that the standard sequential product is not continuouswith the first variable with respect to weak operator topology, order topology and intervaltopology and that the standard sequential product is not order continuous with the firstvariable.We also study the continuity of sequential product on general sequential effect alge-bras and give one sufficient condition with which sequential product is order continuouswith the second variable.