Linear orthogonality preservers of standard operator algebras (Q614492)

Let \(\theta : A\to B\) be a linear surjective mapping, where \(A\) and \(B\) are two standard operator algebras on (real or complex) Hilbert spaces \(H\) and \(K\), respectively. In this paper, the authors give a unified approach to characterize the following linear range/domain orthogonality preservers: (1) \(ab=0\Leftrightarrow \theta (a)\theta (b)=0\); (2) \(a^*b=0\Leftrightarrow \theta(a)^*\theta (b)=0\); (3) \(ab^*=0\Leftrightarrow \theta (a)\theta (b)^*=0\); (4) \(a^*b=0\Leftrightarrow \theta (a)\theta (b)^*=0\); (5) \(ab^*=0\Leftrightarrow \theta (a)^*\theta (b)=0\); (6) \(a^*b=ab^*=0\Leftrightarrow \theta (a)^*\theta (b)=\theta (a)\theta (b)^*=0\). They show that all these preservers carry a standard form, and are thus automatically bounded.