The paper "Automatic Continuity of Biorthogonality Preservers Between Weakly Compact JB*-Triples and Atomic JBW*-Triples" by María Burgos, Jorge J. Garcés, and Antonio M. Peralta explores the automatic continuity of biorthogonality preserving linear surjections between JB*-triples and JBW*-triples. The authors prove that such mappings are automatically continuous when the domain and range are weakly compact JB*-triples or atomic JBW*-triples, respectively, and no infinite-dimensional rank-one summands are present. They also show that two atomic JBW*-triples are isomorphic if and only if there exists a biorthogonality preserving linear surjection between them. The paper builds on previous work by Arendt, Jarosz, and others on orthogonality preserving mappings between C*-algebras and von Neumann algebras, extending these results to the more complex setting of JB*-triples and JBW*-triples. The authors provide detailed proofs and characterizations of the properties of these mappings, including the behavior of minimal tripotents under such mappings.The paper "Automatic Continuity of Biorthogonality Preservers Between Weakly Compact JB*-Triples and Atomic JBW*-Triples" by María Burgos, Jorge J. Garcés, and Antonio M. Peralta explores the automatic continuity of biorthogonality preserving linear surjections between JB*-triples and JBW*-triples. The authors prove that such mappings are automatically continuous when the domain and range are weakly compact JB*-triples or atomic JBW*-triples, respectively, and no infinite-dimensional rank-one summands are present. They also show that two atomic JBW*-triples are isomorphic if and only if there exists a biorthogonality preserving linear surjection between them. The paper builds on previous work by Arendt, Jarosz, and others on orthogonality preserving mappings between C*-algebras and von Neumann algebras, extending these results to the more complex setting of JB*-triples and JBW*-triples. The authors provide detailed proofs and characterizations of the properties of these mappings, including the behavior of minimal tripotents under such mappings.