Spectral representation of infimum of bounded quantum observables

Abstract

In 2006, Gudder [Math. Slovaca 56, 573 (2006)] introduced a logic order ≼ on bounded quantum observable set S(H). In 2007, Pulmannova and Vincekova [Math Slovaca 57, 589 (2007)] proved that for each subset D of S(H), the infimum of D exists with respect to the logic order ≼. In 2008, Liu and Wu [J. Math. Phys. 49, 073521 (2008)] found a representation of the infimum A∧B for A,B∊S(H), and by using the limit methods, they gave out a representation for the infimum of D. But, that representation is complicated. In this paper, we present a simpler spectral representation for the infimum of D with respect to the logic order ≼.