  S. Gudder and, later, S. Pulmanova and E. Vincekova, have studied in two
recent papers a certain ordering of bounded self-adjoint operators on a Hilbert
space. We present some further results on this ordering and show that some
structure theorems of the ordered set of operators can be obtained in a more
abstract setting of posets having the upper bound property and equipped with a
certain orthogonality relation.
