Linear mappings that preserve potent operators

Let H and K be a complex Hilbert spaces, while $\mathcal {B}(H)$ and $\mathcal {B}(K)$ denote the algebras of all linear bounded operators on H and K, respectively. We characterize surjective linear mappings from $\mathcal {B}(H)$ onto $\mathcal {B}(K)$ that preserve potent operators in both directions.