Comment on “A note on the infimum problem of Hilbert space effects” [J. Math. Phys. 47, 102103 (2006)]
Aurelian Gheondea · Journal of Mathematical Physics · 2007
We show that the two main results of the article [J. Math. Phys. 47, 102103 (2006)] have very short proofs as direct consequences of the solution to the infimum problem for bounded non-negative operators in a Hilbert space given by T. Ando [Analytic and Geometric Inequalities and Applications, Mathematical Applications Vol. 478 (Kluwer Academic, Dordrecht, 1999)] and a formula for the shorted operator obtained by H. Kosaki [“Remarks on Lebesgue-type decomposition of positive operators,” J. Oper. Theory 11, 137–143 (1984)].