Spectral representation of infimum of bounded quantum observables

In 2006, Gudder introduced a logic order on bounded quantum observable set $S(H)$. In 2007, Pulmannova and Vincekova proved that for each subset $\cal D$ of $S(H)$, the infimum of $\cal D$ exists with respect to this logic order. In this paper, we present the spectral representation for the infimum of $\cal D$.