Monotone transformations on B(H) with respect to the left-star and the right-star partial order
Грегор Долинар, Alexander Emilevich Guterman, Janko Marovt · Mathematical Inequalities & Applications · 2014
Let H be an infinite dimensional complex Hilbert space, and let B(H) be the set of all bounded linear operators on H . In the paper equivalent definitions for the left-star and the right-star partial orders on B(H) are given and bijective additive maps on B(H) which preserve the left-star or the right-star partial order in both directions are characterized.