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The quantum effects for a physical system can be described by the set  of positive operators on a complex Hilbert space  that are bounded above by the identity operator . For , let  be the sequential product and let  be the Jordan product of . The main purpose of this note is to study some of the algebraic properties of effects. Many of our results show that algebraic conditions on  and  imply that  and  have  diagonal operator matrix forms with  as an orthogonal projection on closed subspace  being the common part of  and . Moreover, some generalizations of results known in the literature and a number of new results for bounded operators are derived

A Note on Sequential Product of Quantum Effects