Curt Healey: Every symmetric Kubo-Ando connection has the order-determining property on unital C* algebra

Recently, L.Molnar studied the question of whether the Lowner partial order on the positive cone of an operator algebra is determined by the norm of any arbitrary Kubo-Ando mean. The question was affirmatively answered for certain classes of Kubo-Ando means, yet the general case was left as an open problem. We here give an answer to this question, by showing that the norm of every symmetric Kubo-Ando mean on unital C* algebra is order-determining.