Automatic continuity of orthogonality preservers on a non-commutative \(L^p(\tau)\) space
Suppose that \(M\) is a von Neumann algebra on a Hilbert space \(H\) equipped with a normal semifinite faithful trace \(\tau\). Denote by \(\mathfrak{C}\) the set of all linear combinations of positive elements \(a\in M\) with \(\tau(\text{supp}(a))<\infty\). The space \(L^p(M,\tau)\) is the completion of \(\mathfrak{C}\) in the norm \(\|\cdot\|_p\). Suppose that \(T\) is an orthogonality-to-\(p\)-orthogonality preserving linear map from \(L^p(M,\tau)\) into a Banach space \(X\). In the paper under review, the authors discuss the automatic continuity of \(T\) for some von Neumannn algebras \(M\).
scientific article; zbMATH DE number 6159669