Tsai, Chung-Wen; Wong, Ngai-Ching Linear orthogonality preservers of standard operator algebras. (English) Zbl 1227.47024 Taiwanese J. Math. 14, No. 3B, 1047-1053 (2010). 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. Reviewer: Wu Jing (Fayetteville) Cited in 8 Documents MSC: 47B49 Transformers, preservers (linear operators on spaces of linear operators) 47L10 Algebras of operators on Banach spaces and other topological linear spaces Keywords:linear orthogonality preserver; standard operator algebra; autocontinuity PDFBibTeX XMLCite \textit{C.-W. Tsai} and \textit{N.-C. Wong}, Taiwanese J. Math. 14, No. 3B, 1047--1053 (2010; Zbl 1227.47024) Full Text: DOI