Abstract:
Let B(H) be the algebra of all bounded linear operators on a complex Hilbert space H with dim H≥3. All the bijections on the set of all partial isometries on H which preserve the order and the orthogonality in both directions are described,which answers the question raised by Molna＇r in 2002.As an application,it is shown that an additive surjection φ on B(H) preserves partial isometries in both directions if and only if one of the following assertions holds:There exist two unitary operators or two anti-unitary operators U and V on H such that (1)φ(X)=UXV X in B(H),(2) φ(X)=UX*V X in B(H).
